If I use my Kharox to play a mixologist from opponent trash. When mixologist die, can I still use the effect of it or it will be returned to opponent before it trigger deathknell effect

Yes — you still get the Deathknell. The trigger is created and placed on the chain as a Pending Item before the card ever leaves the board, so it resolves normally even though the card itself ends up in your opponent's trash (Rules 808.1.d.2 / 428.1.a.1.b; cards always go to their owner's zone per Rule 56).

You control the Mixologist, so you control its Deathknell — same principle as stealing a Deathknell unit with Possession (FAQ #4896: controller gets the trigger, card goes to the owner's trash). Note the ability reads "play a unit from your trash," so "your" means you: you must have a legal unit (cost no more than [3] and no more than [A]) in your own trash, not the opponent's.