Revivify

While spells like Raise Dead and Resurrection specify that the target needs to not have been Undead, the spells True Resurrection, Reincarnate, and Revivify do not. This mean that a creature turned into undead can still be raised back to life with these spells. If so, I would assume the spells bring back the creature to full life instead of raise them as Undead again.

Does the “creature that has died within x time limit” parts of the spells refer to the creature in their original state or does dying as an Undead count for the spell requirement?

A Life Domain Cleric casting Revivify should be able to apply the Disciple of Life Feature Bonus to add 2 plus the spell slots level to the amount of Hit Points restored. Cast with a 3rd level spell slot, a Life Domain Cleric should revive the creature with 6 Hit Points.

Level 3: Disciple of Life

When a spell you cast with a spell slot restores Hit Points to a creature, that creature regains additional Hit Points on the turn you cast the spell. The additional Hit Points equal 2 plus the spell slot’s level.

Definitely the case for True Resurrection that the deceased is brought fully back to life as their previous creature type. Reincarnate creates a new body for the deceased, so you could have a case where their former body could be wandering around as a zombie or ghoul.

As for Revivify, technically RAW written it's correct it could reverse undeath, but practically there are few cases where the creation of an undead takes less than a minute, and thus the time limit on Revivify would have already passed. The spells Animate Dead and Create Undead take a full minute to cast. Undead created by monster attacks often take more than a minute as well. A wraith's Create Specter ability can race against the clock with Revivify. Create Specter requires the corpse of a person who has been dead less than a minute. If a wraith used this ability with at least a round to spare before the minute ran out, someone could reverse the effect with Revivify. The effect clearly states the specter rises in the same space as its corpse, and so the deceased remains present for a caster to touch.

This need to clearified it needs to be a mostly intact body so you dont have folks arguing you can revivie a body part

wait dead creature? not dead humanoid? why is the restriction on who you can cast spells on so arbitrary? like this third level spell can be cast on any creature at all, but I can't cast hold person on a cat because they are not a person? ridiculous how made up these rules in lore. 

"yes you can revive a dragon, but you can not hold the dragon still, even if the dragon IS SHAPED LIKE A PERSON, their still not one."