Alchemist Aprentice and Sacrificing clarification

[PrinceCharming]

Im still fairly new to competitive magic, so I'm sorry if this question seems a bit silly.
In regards to Alchemist's Aprentice (sac: draw a card), I am wondering if I am able to sacrifice him in response to him being killed.
While I am aware that block/sac before combat damage is a thing, my concern is if he were to be given -1/-1, (which would kill him) am I able to sacrifice him in response?

The specific example involves Havengul Lich and Heartless Summoning. With both those cards on the battlefield, I am able to cast Alchemist's Aprentice from the graveyard for 2 mana. The plan from there is to immediatly sac him for a card draw.
I'm not sure if this is possible, as heartless summoning would give him -1/-1 as soon as he came into play.
If anyone can clarify this, that would be great.

Cheers.

[Phat Max]

You can always sac him in response to anything, because everything uses the stack.

Someone cast {dismember} targeting Alch
You sac Alch in response

This your sac goes off first, and makes the {Dismember} fizzle, since it's target no longer exists.

[PrinceCharming]

So then my little card draw combo would work?
Thanks for te clarification!

[JaCe BeLeReN]

{Alchemist Aprentice}

[Phat Max]

Oh dang, somehow I overlooked the {Heartless Summoning} part of your post...

With that out, your Alch will ETB with 0 toughness, which will send him to the GY as a state based effect. You can't do anything in response to state based effect.

Sorry bout that

[scarsabrex]

Oh dang, somehow I overlooked the {Heartless Summoning} part of your post...

With that out, your Alch will ETB with 0 toughness, which will send him to the GY as a state based effect. You can't do anything in response to state based effect.

Sorry bout that

resolved

[PrinceCharming]

Ah, dang. I thought I was on to something there. Appreciate the help!