If I am not misunderstanding, it should be in the actions for the object itself? Rather than an action under System, I mean.
"Destroy" is the name.
Depending on what you're doing, you might also be able to use three or four animation frames for your health sprite, with the animation speed set to 0, then just change the frame.
It would also be possible to destroy an object by unique ID or object ID, using "pick by comparison", but is only needed if you have multiple instances of one sprite object (all having the same name/object ID, I mean).