If a unit is dealt damage and then a buff is removed from it, does it die?

Yes, the unit will die.

Removing a buff reduces the unit's Might by 1 (Rule 703: each buff gives +1 Might). When non-zero damage marked on a unit equals or exceeds its current Might, it is killed (Rule 143.2.a). So if a 3-Might unit with a buff (effectively 4) takes 3 damage and then its buff is removed, its Might drops to 3 — and the 3 damage now equals its Might, killing it. The death happens during the next cleanup (Rule 323.5).

This is consistent with FAQ rulings: reducing a damaged unit's Might below or equal to its marked damage kills it (FAQs #5491, #2662, #3401). The same principle applies whether the Might reduction comes from a spell, an ability, or removing a buff.