I take away that "rolling an extra d20" nonsense. The odds of that happening are so low anyway, why not just make it lop off a limb whenever you roll a 20? It's a Very Rare magic item. It should have an appropriately awesome effect that you'll see more than once every 400 attacks. And imagine if you did roll two natural 20s on a creature you had already killed from the additional 14 damage and it wasn't even a powerful creature.

I might make it a 50/50 just because chopping of a limb is very very detrimental.

I mean, if you did it against a boss creature on the first round of combat, yeah, it would make the fight easier, but most of the time it's going to be against monsters that are probably going to die from other sources of damage in one or two rounds anyway.

If you were concerned about that, I think you could easily take a leaf out of the vorpal sword:

A creature is immune to this effect if it is immune to slashing damage, doesn't have or need [limbs], has legendary actions, or the GM decides that the creature is too big for its [limb] to be cut off with this weapon. Such a creature instead takes an extra [~]6d8 slashing damage from the hit.

The item description refers to "GM" instead of "DM".

In my campaign there is a weapon that is a +3 Longsword of Sharpness. The way I play it is upon a hit, max your damage; if the roll is 17+ add the 14 points and grant the crit, then roll the confirming d20 and on a natural 20 there goes the limb. While yes, it could be overpowered, but is considered a very rare weapon, and for the sake of balance there are very few of them, as they are wielded as an extension of shadow/human hybrid creature, and disappear within a minute of the creature's death. I am a very experienced player/DM, but very new (a few months) to 5e, and would appreciate any input.

Thank you for your time.

Why does this weapon not have a bonus to hit or damage?  1 in 400 chance to cut off a limb, which achieves no discernable benefit, does not make this item worth a very rare tag along with an attunement slot.  This sword is rare at best. This is such poor game design.  Just awful.

Quote from Gath1965 >>

In my campaign there is a weapon that is a +3 Longsword of Sharpness. The way I play it is upon a hit, max your damage; if the roll is 17+ add the 14 points and grant the crit, then roll the confirming d20 and on a natural 20 there goes the limb. While yes, it could be overpowered, but is considered a very rare weapon, and for the sake of balance there are very few of them, as they are wielded as an extension of shadow/human hybrid creature, and disappear within a minute of the creature's death. I am a very experienced player/DM, but very new (a few months) to 5e, and would appreciate any input.

Thank you for your time.

 
I think this is fine if it suits both you and the players. However, the rule regarding activating the additional damage or special effect is clear: "The sword of life stealing activates when you roll a 20 on the d20. The same is true of a vorpal sword."

Ref. https://twitter.com/JeremyECrawford/status/752583305506070529

does the extra damage only come when u roll a NAT 20 or just a 20. I'm assuming nat 20 but it doesn't say😭

It’s 20 on the roll so nat20. 

Is it just me or is this like. terrible?