After playing a unit with Glasc Mixologist Deathknell, does the HP reset?

Yes — the unit you play from the trash enters with no damage marked on it, and any damage on your surviving units was already healed before the trigger resolved.

Damage doesn't persist on cards in the trash, so the new unit enters fresh. And in the standard case (Mixologist dying in a Combat Showdown), Combat Cleanup heals every unit in play before the Deathknell trigger is finalized and resolved, so you can't use the trigger to "finish off" an enemy that survived combat — they're already healed to full by the time your unit arrives (Rule 461.1.a.1). This is also why Mixologist's Deathknell can't save a unit that already took lethal damage.

One caveat: the automatic heal only comes from Combat Cleanup (or the end-of-turn heal). If Mixologist is killed outside combat, nothing is auto-healed — but the newly played unit still enters with zero damage either way.