Here's question I just dreamed up.

Ok, so lets say my opponent has an Eternity Vessel on the field. And lets give it 14 charge counters.

I have a Vampire Hexmage on the table, my opponent plays a land, activates the Eternity Vessels ability. I sacrifice Vampire Hexmage while the Vessels ability is on the stack, removing the 14 counters. Does that kill my opponent or can he cancel the ability?