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Based on the FAQ at http://tools.kingdomdeath.com/faq/ the mood cards are not counted as anything while they are in play:

►Do survivors need to remove a monster's in-play Mood or Trait cards to defeat it?
No. A monster is defeated when it is wounded and there are no cards in the AI deck or discard to move to the Wound Stack (pg.217, Core Game Book).

If the mood is active, the AI and AI discard pile is empty, and the monster is wounded, then it's dead; it's just a very Bloodthirsty corpse. However, if the mood is removed from play but not archived, I believe it goes back into the discard pile and would need to be removed so long as it wasn't drawn and put back in play, where it would no longer count again. I'd have to review the Bloodthirsty card to see what it actually says (archive vs. discard) though.