Quote from gathraawnOnce Ajani resolves, since it's your turn, you gain priority again to use one of his abilities. He can respond by sacing the Hexmage, which should kill Ajani, but since his ability is independant of his survival, it will still resolve.
Quote from stereosoundTo continue this question, I just want to clarify my understanding of the stack:
My understanding was that the spell itself went on the stack, is this incorrect?
EG: (hexmage on field)
1. Garruk played, it goes on stack
2. Both players pass priority, spell resolves
3. Active player passes priority, I sac hexmage targetting garruk, pass priority
4. Both players pass priority, hexmage effect resolves
Essentially, does the stack end at step 2, so that there's not a chance to use the stack after the spell resolves? (Unlike an effect/ability, ala countering Demigod so he doesn't return to play)
Quote from AngeliqueFor that moment, it would stop at 2 when Garruk resolves. With you being the non-active player, you don't have priority at that time and your opponent (with priority) can activate an ability of Garruk's before you can even sac the Hexmage.
However, if he decided to not use Garruk's ability and went onto the next phase, then you'd be passed priority before moving onto the next phase and that's when you could sac the Hexmage. The situation that you described would be simular to this.