If you play in the Merry Band of Misfits server on discord don't read this. 

Master's Amulet doesn't actually grant a shield guardian, it just lets you control the guardian that it is linked to it.

Also, as the DM, you have final say over characters, and there was an implied "within reason" I am assuming for the magic items they could take. If this is causing balance problems, then ask the player to pick again. If they don't, I would kick them.

I think you need to include more enemies that deal status effects instead of just straight damage. Hit him with confusion... polymorph his pet into a cow... create walls of fire that limit mobility on the battlefield. Give the enemies more opportunities to heal themselves. If they're facing against undead monsters, maybe add fonts of necrotic energy to the battlefield that heal the undead each round. Maybe make them mechanical objects that need to be dismantled instead of just smashed, so this character needs to spend at least a round or two disabling it instead of relying on sheer damage.

You could try throwing an Earth Elemental at them and fudge the rules a bit so that it deals double damage to the Shield Guardian. You could also just take one of the magical items out of play: you could destroy the Master's Amulet or maybe have it stolen by a pickpocket. Destroying the amulet will take the Shield Guardian out of commission for a while, whereas having it stolen creates some interesting conflict.

I also have this one funny idea where, during some point in combat, the Shield Guardian suddenly develops self-awareness and has an Existential Crisis, becoming completely useless for the duration. It'd probably be a one-off, but it would definitely be hilarious.

The rogue characters comment about gettig unpleasant if they dont revivify the guardian is a shame, out of interest did they have a story reason to have the guardian? If they stole the amulet then it is only reasonable the wizard that made it will come looking for it and bring the full weight of their magical prowess down on the rogue.

Given the amulet wearer and shield gauardian need to be within 5ft of each other then they are open to area effects, Fog Clouds, Grease, Spike Growth etc will take their toll as the Rogue will need to stay close by if they want the AC buff each turn.

The Shield Guardian only has a dex of 8 so any saving throw that targets dex will work more often than not,. If you did want to go all out to remove it then a Sorcerer using Quicken spell to chill touch and distinergrate in the same round would be the easiest way, chill touch will stop it regenerating and disintergrate targets dex saves and deals stupid amounts of damage.

EDit: 3 words to strike the Rogue dead...Power Word Kill, a tad over kill but if all else fails.

Other option for a spell caster would be teleportation effects like scatter, banish or planeshift to move them more than 60ft apart to deny them the life sharing aspect, even spells like gust of wind, levitate and bigbys hand could push them apart. Hold Person on the rogue effectively takes them both out of a fight.

Non-magical option: I assume they are strutting around town with it so have a local crime lord offer them a vast sum of money for the shield guardian and if they refuse have the crime lord steal the amulet and give the Rogue a quest to try and retrieve it, this would also give the rest of the party an "out" if they don't enjoy the guardian being involved as they can just say "we're not helping".

Reading about the Master's Amulet... it's interesting because it is one of the rare magic items with a statted AC and HP. It also seems to not require attunement. If the enemy knows he has it, it's reasonable that they'll be trying to steal it from him, either to take control of his guardian or just to destroy it outright. Send some of your own rogues after him with eyes on that amulet. If he manages to hold onto it he'll probably double up defense on it... attaching it to a lock on his belt or something, or being really adamant about how well hidden it is on his body, but at the very least you'll make him aware that the amulet itself is as much of a potential liability as it is a boon.

I think going for the amulet being attacked would work quite well, it would take the shield guardian out of commission for a while without permanently removing it. It would also make him realize that the amulet could be a liability as he'd have to be worrying about it being destroyed at all times. And if he decides he no longer wants it, I can always trade the item for a less broken rare magic item. It might just cause him to double down, though. 

Thank you all, for the great advice.

As for the story reason for him having the amulet, we decided that he got it from the cult of the burning blade (Zariel) when they attacked their headquarters during the timeskip between level 5 and level 10.

Well if they got it from a cult then its only reasonable for the cult o come calling to retrieve it...or Zariel turns up with a couple of devils and wants her trinket back...or the Rogue can keep it for the cost of his soul, which means no raise dead or ressurection or revivify for him if/when he dies.

There are lots of options for getting around a shield guardian; for example, Banishment it and kill the rogue in the interim. Or, somewhat oddly, Confusion actually works on things that are immune to charm.

I would also consider just killing the shield guardian in a way where Revivifywon't help. You could just rule that the spell doesn't work on constructs at all because they aren't alive and therefore don't die, they get destroyed. Or you could annihilate it with an effect such as a mace of smiting (which destroys its target, rather than killing it) or disintegrate.

It sounds like you have a problem player, but the DM is not required to be fair.

 I wouldn't call the rogue overly powerful. What level is he?

I used to have a guy in my game who specialty was Min/MAX 👀

The monsters I mean is characters killed every encounter and the group was there to see is awesomeness. But you say EvilDM that must be boring for the other players.

The minute they express their felling plan B was up and running! 😁

The reputation of is character for killing/destroying enemies was now high so the enemies started to pay for spells or poison to make his STR goes to 1 for 3d6 rounds until he was killed by an assassin blade.

The players player played is PC for 12 sessions plan B was sessions 7

We have a talk and I said to him that was my limit of min/maxing he got the message and all is next PCs was more balanced fearing my wrath 😆

YMMV 🙄

Sounds like you gave them way too many overpowered magic items. A nice overrun of the party to have them captured instead of outright killed and have them stripped of their magic items would balance things out quite nicely. Allow them the ability to get them back at increasingly difficult levels based on the item. The lower powered magic items like a spellbook could be in with normal equipment when they escape but the shield guardian and belt of giant strength could be with the BBEG. Now they have to decide if the OP loot is worth the trouble at their current level, or to circle back to retrieve when the items are level appropriate.

I asked them to take a different magic item, but they refused because I told them they could have any magic item when they asked.

I am sorry, but no.

You are the DM. You have final say over everything. You shouldn't be a jerk about it, but if you say, "Look, I know I told you any item but NOT THAT -- it's Overpowered," then the player either accepts that or leaves the game. Players do not get to overrule the DM. Ever.

You need to speak to the player out of game, and tell them that this is making your job impossible, and as a courtesy to you, that you need them to give up the shield guardian. If they weren't supposed to have it with the amulet in the first place, even better - now you have RAW behind you. But I don't really care about RAW here. I care about the player showing respect to the DM. And common courtesy as well.

Clearly your mistake was in giving them pick of magic items from the book. Never, ever do this. Instead, write down a list of magic items slightly larger than the size of the party x the number of items you want them to have, and say, "Choose from among these." Not "any uncommon" but "these uncommon." So if there are 6 players, give them a list of 8 "very rare" items that you have vetted as not being campaign breaking, and let the party choose from among that list. The hand them a list of 8 rares, same thing. Then 14 uncommon, same thing. This will ensure that you only have magic items YOU want in the campaign, and these will then not unbalance things (assuming you know how to pick them). Also, it will require the "min maxer" to negotiate with the other players. Maybe multiple people want that belt of hill giant strength, for example.

As the DM, you should control 100% of the magic items in your game. Never, ever, let anyone, including the dang-blasted dice, decide what item goes in your game. You should carefully scrutinize everything -- and I mean everything, I don't care how "weak" it looks -- to ensure that it will not screw up the challenges you have planned for your party. Magic items are fun to have and you should give them out -- but they must not trivialize the adventure content. Your MMer is using his obscene item picks to trivialize your adventures. This is not a good situation and it must be stopped.  And stopped NOW. Do not allow it to continue just because "it's too late." It's never too late. 

If you want to grease the wheels a little, make a list of 3-4 magic items of the same rarity but which you have vetted as not being unbalancing. Offer the MMer the option of replacing the Shield Guardian and the amulet it rode in on, with one of these. Alternatively, the MMer can just lose it period, and get nothing in return. Min-maxer's choice.

But do not allow a player to run roughshod over your campaign like this. It needs to stop, now, or you will just have increasing misery.

I agree with BioWizard. If you are having a hard time with the item choice, talk to your player. Although...

You gave the rest of the players access to a very rare item, and none of them "broke" your game? That's a Mirror of Life Trapping. That's a Nine Lives Stealer. That's a freaking Staff of Power. Your player spent his very rare item on a Belt of Fire Giant Strength. He's a rogue with a ~7d6 sneak attack, he spent his very rare item on +2 attack and damage, and you're complaining about one of his rare item choices?  He gave you a gift, my friend. Do you know how gamebreakingly powerful Nolzur's Marvelous Pigments are?

If you decide to let him keep it (I would), then just play to his strength. His shield guardian makes him unkillable and invincible? Fine. Don't target him. Any half-competent creature sees a shield guardian and knows the score. Why waste time attacking him when it doesn't DO anything? Instead, target everyone else. He'll feel like he really pulled one over on you until he realizes that he's reaping none of the benefits of his pet. It does an extra 11-22 damage per turn? Okay, whatever. Soak it, and focus fire on the party fighter. Want to really mess with his head? Throw a few rogues at him, and remind him what he's missing. Have one of them straight up disengage him and make a beeline for the party caster. Heck, rub salt in the wound, and have two of them do it. Two rogues in melee range means both of them get sneak attacks, and suddenly, he's running around the battlefield trying to keep his party alive. Except no, he can't run around too much, because he has to stay in range of the shield guardian, or everybody will gang up and kill him while he's unprotected.

This isn't a punishment. This isn't you being "unfair" or "picking on him." This is how his choice affects enemy combat tactics. Put yourself in a player's shoes. You show up to a fight, and there's a boss and 3-4 henchmen. The boss has something that makes him nigh-unkillable - it would take all your attention to whittle them down. Do you spend ANY time on the boss? Maybe you throw a Hold Person on them, but you're going to get rid of their henchmen first. Then, when they're down, you find a way to take away whatever makes them "invincible," or just sit there and whittle away at their health until they finally succumb. 

After two fights like this, he's going to sell that amulet to the nearest passerby. Either that, or you'll realize that the rest of the party is balanced to the same power level, and they'll handily manage without him. Then you can just scale up combat to continue to provide a challenge, because your player isn't OP after all.

The amulet has AC and HP, so i'll destroy it in the next fight and then if he wants it back he'll need to spend all 1,000 gp he has to recreate it. If he doesn't want to do that I'll give him the choice to pick from a few good rare items that don't break the game.

Also, the argument that he could've broken the game more, but he chose not to so I should be thankful doesn't really work because he still broke the game rather horribly and then refused to change his item when I asked him to. I know for a fact the rest of the party isn't as powerful because they got the implied within reason. The second most broken character is the paladin, but he's only really broken because of his AC, but due to the party having good ACs I can just raise the monsters' to hit which makes balancing for that easy. Balancing for a character that is the best DPS class in the game and also is now as good of a tank as a totem warrior barbarian is a lot harder.

I think the larger issue here is... you trusted your players to pick items that would not break the game, and Min-Maxer picked one that was OP... which maybe they didn't realize. But when you explained it to MMer and their answer was basically "tough noogies," that is not acceptable.

What this tells me is that, although you trust your players, this one, at least, is not trustworthy. That is a much larger issue than the shield guardian. You need to be able to trust your players, and they you. If you cannot, something is deeply wrong and this needs to be handled now.

I play via VTT/Google Meet only. My friends are all over the continent. Sometimes they roll in the VTT, but that has been and will always be optional. Some people like rolling physical dice. I trust them to tell me their rolls truthfully. There is no point to bothering to play a game with dice if you are going to lie. So I let them roll and tell me their rolls. I trust them.

If I couldn't trust them to do that honestly, I wouldn't play with them at all. If I need to "see the dice" to confirm the roll is honest... again, I wouldn't even play D&D with them. You need to be able to trust the people with whom you play D&D.

If this player is not going to be trustworthy, that is a much larger issue, and conversation, than just the magic item. The item is a symptom of the problem, not the actual problem.

Going off the story that's been told so far, I do agree that there's a serious potential problem with this player.

For one, as BioWizard mentioned, openly defying the DM is a bad sign. For two, OP mentioned that, when the question of just killing the Shield Guardian came up, none of the other players were interested in reviving it, and the MM made it clear that they would make things unpleasant for the other players if they didn't. That's a serious conflict. It's clear from the other players' reaction that they are having less fun because of the Shield Guardian and would be happy to see it gone. But that the MM openly threatened the other players with a bad time if they don't get their way is a big red flag. 

Yes, I forgot to mention that, but Transmorpher is right. Players threatening other players is not cool. (Characters can do it, as long as everyone at the table is friends and OK with it, but players vs. players, no.)

Another thought, that rogue is built for melee combat.  He's severely limited in ranged combat, especially against intelligent opponents who use cover.  Hit and run combat where the opponents stay out of melee range and use cover is a fun change of pace at times and that tactic will hinder him.  As a player I've ducked in and out of a Fog Cloud before and it was very effective!  Why should PC's have all of the fun?