If I cast Mind Spike and am concentrating on it, then cast Create Bonfire, I can maintain my concentration on Mind Spike, right?  It doesn't automatically force me to break concentration just because I cast a second spell with a duration of concentration?

Yes, it absolutely does force you to break concentration. That's the entire point of concentration. You can only concentrate on a single spell at a time. Casting a second concentration spell immediately breaks your concentration on the first.

Sorry, it seems I missed part of what I intended to ask- can I cast Create Bonfire without concentrating on it to maintain concentration on Mind Spike?

Since Create Bonfire deals damage immediately when the spell is cast am I able to simply cast it as if it's an instantaneous spell and not bother concentrating on it so as not to lose the spell I'm already concentrating on?

Quote from 6thLyranGuard >>

Sorry, it seems I missed part of what I intended to ask- can I cast Create Bonfire without concentrating on it to maintain concentration on Mind Spike?

Since Create Bonfire deals damage immediately when the spell is cast am I able to simply cast it as if it's an instantaneous spell and not bother concentrating on it so as not to lose the spell I'm already concentrating on?

No. You cannot cast a concentration spell without concentrating on it. That's what a duration of concentration means. Even if you could, it would have no effect, since the spell's description says that its effect lasts "until the spell ends," and concentration spells end when your concentration ends.

Per the description of Create Bonfire:

Any creature in the bonfire's space when you cast the spell must succeed a Dexterity saving throw or take 1d8 fire damage.

That's not an effect that requires you to maintain concentration on.  Because of that, it seems like you should be able to cast the spell without being forced to maintain concentration.

Quote from 6thLyranGuard >>

Per the description of Create Bonfire:

Any creature in the bonfire's space when you cast the spell must succeed a Dexterity saving throw or take 1d8 fire damage.

 

That's not an effect that requires you to maintain concentration on.  Because of that, it seems like you should be able to cast the spell without being forced to maintain concentration.

You can certainly cast it without maintaining concentration. There's no lower limit on how long you can concentrate on a concentration spell (aside from 0, I suppose). But you can't cast it without concentrating, even if it's just for an instant, because the duration is concentration, not instantaneous. Whether or not this should be the case is a different question that I don't really have an opinion on. Here's the rule on casting concentration spells:

You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once.

The moment you begin incanting the Create Bonfire spell, you lose concentration on whatever else you might be concentrating on.  That is how concentration spells work.  The moment you begin casting another concentration spell, your concentration on a previous spell fades.

And suddenly, Create Bonfire became a whole lot more useless.

It isn't useless in and of itself, just what you intended for it.  Perhaps you should look into produce flame instead?

One, Produce Flame isn't on any spell lists with Mind Spike.  Two, it's only got a range of 30 feet.  Three, it's an attack roll and not a saving throw.

There are ways to get spells that aren't on your class' spell list. But what should also be pointed out, in case this was your intention, is you cannot cast both Mind Spike and Create Bonfire on the same turn as each spell requires 1 action. 

If you want a cantrip to cast while concentrating on Mind Spike and you want it to have a saving throw consider Frostbite, Mind Sliver (if your DM allows Unearthed Arcana),  and Thunderclap. 

I didn't ask if I could do this in one turn.  And if I wanted to, there are potential ways to do so thanks to various abilities that turn a spell's casting time from an action to a bonus action.

Also, I'm quite aware of all my options for damage-dealing cantrips.  None of the other ones applied to the scenario, so there was no need to mention them (and for the record I'd go with Toll the Dead).

Out of curiosity what was the scenario? Why did you want to specifically use Mind Spike and Create Bonfire?

A fight with a Flesh Golem in a fog cloud.

Quote from 6thLyranGuard >>

A fight with a Flesh Golem in a fog cloud.

 I'm not sure that the combination would work the way you want in any case.

1) Casting Mind Spike requires you to see your target "You reach into the mind of one creature you can see within range." .. so it would have to be cast before the fog cloud.

2) Create Bonfire also require you to cast it on ground that you can see within range "You create a bonfire on ground that you can see within range." This also does not work in a fog cloud

3) Mind spike lets you know where the creature is and prevents it from hiding:

"On a failed save, you also always know the target's location until the spell ends, but only while the two of you are on the same plane of existence. While you have this knowledge, the target can’t become hidden from you, and if it’s invisible, it gains no benefit from that condition against you."

It gains no benefit from being invisible. If the create was invisible then as a DM I'd allow spells that require you to see the creature to be cast against it since MInd spike clearly states that invisible creatures gain no benefit from that condition.

However, in your example, the creature is in a fog cloud and you still can not see the creature if it is in a fog cloud.So even without the rules on concentration, this combination would not have worked anyway.

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As for concentration ... PHB p203

"Casting another spell that requires concentration. You lose concentration on a spell if you cast another spell that requires concentration. You can't concentrate on two spells at once."

The rules are pretty explicit. If you start casting a spell requiring concentration then you lose concentration immediately on any spells you are currently concentrating on.

RAW, the answer has been stated pretty clearly. But I think this is something that many DM's would be willing to homebrew, since the damaging effect of Create Bonfire is instantaneous. Definitely something worth discussing with your DM, you just have to approach it from the angle of asking for a deviation from the rules.

Yes, being able to see the flesh golem is necessary the first round.  I have GM-approved ways to do that.

Have you considered oil and a torch? If you have Prestidigitation you can light your torch with one action.

People, I had a question about the rules.  I am not looking for alternative ideas, I'd have posted somewhere other than the rules page were that the case.

Quote from 6thLyranGuard >>

People, I had a question about the rules.  I am not looking for alternative ideas, I'd have posted somewhere other than the rules page were that the case.

Pardon, I was trying to be helpful. I hope you'll forgive me that impulse. You've gotten your answer according to the rules. A spell with a concentration duration requires your concentration to cast and to maintain. Casting another spell with a concentration duration while you have one such active makes your first spell fail. Rules are pretty clear.