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If someone was attempting to stretch another character (for example, a giant pulling them apart with their head in one hand and their legs in the other) then what roll would the attacker/attacked need to make and what damage type would it do?
Wouldn't it result in an instakill for 90% of characters if they got dismembered this way?
This is related to the concept of called shots (see other questions here and here). The summary of those answers, and the relevant portion for this question, is that creatures are unable to make attacks that somehow subvert a target's hit point pool. I won't re-hash the excellent reasoning given in those answers, but I will add a few points of my own that I did not catch in a brief reading:
Narrative Justification
Hit points are not a direct representation of "health"; as per the PHB p.196,
Hit points represent a combination of physical and mental durability, the will to live, and luck.
In general, you cannot make an attack or cause damage that kills a player without reducing their hit points, because those remaining hit points represent the fact that they have resisted death from that effect.
For example, in your given scenario of a giant attempting to pull someone's head off, the fact that the player has not been reduced to zero hit points may represent the fact that they have enough energy to squirm free of the grasp, or to pull out their weapon and stab the giant's hand, dealing no damage but proving distracting enough to avoid dismemberment.
Killing Blows
But perhaps you like the idea of pulling somebody's head off to kill them. This is a fantasy game, after all, and maybe you want dramatic moments. What to do?
The solution is simply to reflavor killing blows as whatever dramatic effect you want to achieve. If a PC is already dead, or you land a blow that fully kills them, then you can flavor that blow however you'd like- in this scenario, as the giant pulling the character's head off, or ripping them clean in two.
With that said, you should still be somewhat cautious about this. You should, for example, avoid destroying the PC's body entirely, unless an ability explicitly says so, as the state of a player character's body does have mechanical effect on how easy it will be to resurrect them.
Mundane Attacks
The bulk of my answer has focused on the mention of dismembering by stretching; however, in the case that you wish to stretch a character without the effect of instant death but still causing damage- the closest official attack available to all creatures would be an unarmed strike (PHB p.195), which would deal bludgeoning damage equal to 1 + the attacker's Strength modifier.
A DM may adjudicate otherwise, of course, but there is no official guidance on damage taken from being stretched.
I'm not going to even pull it off the shelf, just paraphrase from memory:
Going on, that section will describe attack rolls in a way that makes it pretty clear that attacks aren't likely the right paradigm for this situation.*
But you probably want to give your PC a chance to not die, so think about a saving throw. Or three. One to avoid getting grabbed in the first place, one to try to squirm out, one to try to resist the dismemberment long enough to buy just enough time for yourself or another to take an action directed at changing the situation.
At this point there are a bunch of judgment calls you're having to make: how many save-chances, what difficulties... all of which are goign to be informed by your table's playstyle. Are your heroic PCs sure they'll survive even this, and the fun's being had playing to find out how and generate the great war story? Are your gritty PCs resigned to their faux-"realistic" fate?
I don't think we can answer those questions for you. But the tools are there in the game for you to create the scenario you envision.
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* - except, honestly, attacks aren't that crazy here, either. A giant ripping my head off could easily be a grapple and then a kill. And there are some existing examples to look to, like the Giant Toad. Or the Tarrasque. Note that the tarrasque's bite attack includes a grapple, and then when grappled the Tarrasque can swallow, inflicting boatloads of damage on the creature. In your case, it'd be pretty easy to stat up a "grab" attack that does nominal damage and inflicts a grapple, then an ongoing lotsa-damage due to stretching until the grapple's broken.
It seems that "if there is no power for it, there is no real rule for it". However if you need something to roll, you could just handle it as a unarmed attack against a enemy the attacker has grabed. (There should be rules for that, but I could not find them in link- or quoteable form. There were rules for it in previous versions. But given 5E's track record, they might have had to remove those for balance/consistency reasons, so I will not bet on it).
That the character is stretched would then just be a flavorfull description or special effect with no game meaning, on how this damage is done.
Of course you may want or have to write a abiltiy for that. Unless some other poster finds something for it you would have to design and balance it yourself from scratch. Attacks that cause or require a running grab like a Constrictor Snakes "Constrict" might be a good starting point. Unfortunately it is a "cause Grab" and "must release to use against anyone else" ability, not a "must have grabbed the creature" thing. The only ability I could find that actually requires a grab is Swallow - wich is unfortunately far to different in purpose to really properly use here.
