Can I use path to exile in response to someone sacrificing a vampire hexmage to prevent removal of counters?
Can I use path to exile in response to someone sacrificing a vampire hexmage to prevent removal of counters?
no. The sacrifice is part of the activation cost so you won't have a chance to respond until the activation is paid for and the effect is on the stack.
Think of activation's like this...
Person A pulls a gun and fires a bullet at person B.
Seeing the Gun being pulled out Person C fires a bullet at the gun in Person A's hand.
The bullet from person C's gun hits the gun and knocks it out of person A's hand.
You question is equal to "Does that stop the bullet that's on it's way toward person B?" and the answer is no. Just because you took out the source of an effect doesn't stop it's ability from trying to resolve any more than you can stop the bullet en route to person B.