What happens to your original form when you lose body parts while under the effect polymorph or alter self?

Question

As an example, let us assume someone cuts out your tongue while you are in either polymorph or alter self. What happens when you change back? Do you regain your tongue? Does the cut-out tongue disappear?

Answer 1

For polymorph, no parts missing

Whilst it's not explicitly spelt out in the spells description, we do know that you can reduce a creature's polymorphed form to 0 hit points and not injure the creature's "true" form.

From polymorph, PHB p. 266:

The target assumes the hit points of its new form. When it reverts to its normal form, the creature returns to the number of hit points it had before it transformed. If it reverts as a result of dropping to 0 hit points, any excess damage carries over to its normal form.

From this, it must be assumed that any damage this "new form" takes does not affect the "normal form" (excluding the carry-over damage if the "new form" drops to 0 hp). Otherwise, everyone who had ever been polymorphed would be covered in injuries upon reverting (even without being reduced to 0 hp) if their polymorphed form had taken any damage whilst they were polymorphed.

From this, we can infer that parts missing from the "new form" do not affect the "normal form" in the same way that less significant injuries do not affect the "normal form" (excluding carry-over damage).

For alter self, missing parts as normal

Alter self is a lot more limited in the new form that it grants you. You can either change your appearance or grow a few extra bits (such as aquatic adaptation or natural weapons).

From alter self, PHB p. 211:

Aquatic Adaptation. You adapt your body to an aquatic environment, sprouting gills and growing webbing between your fingers. [...]

Change Appearance. You transform your appearance. You decide what you look like, including your height, weight, facial features, sound of your voice, hair length, coloration, and distinguishing characteristics, if any. [...] ... your basic shape stays the same; if you're bipedal, you can't use this spell to become quadrupedal, for instance. [...]

Natural Weapons. You grow claws, fangs, spines, horns, or a different natural weapon of your choice. [...]

If you merely change your appearance, you're still you (as it says you still keep your basic bidepal shape), so your arm or tongue may look different but it's still your real arm or tongue. If you lose it, it would be the same as if that were to happen whilst not under the effect of that spell.

For extra bits, as I've called them, since it's implicit that the extra bits you grow (like gills or claws) would disappear once the spell ends, if you lose a gill or a claw, since you're unaltered form never had those parts to begin with, I'd say there's no damage to your true form (aside from whatever hit points your DM would say you might lose from having, say, a claw ripped off), although a DM may also claim you have a scar where your claw was ripped off or whatever, but this would be purely aesthetic.

The removed parts themselves would probably disappear

Since the removed tongue or Claw or whatever was created via magic, it would make sense that when the spell ends these parts would cease to be, same as if they had not been ripped off or whatever.

See also: Do removed parts of a Druid's Wild Shape form persist after said Druid exits Wild Shape? (thanks KorvinStarmast)