I think… death for him is anything that can be considered as death..
Anything, so like destroyed, stop moving, soul dispersed, stop breathing, or even vanish itself , until it's truly death
example, if it's a normal human, applying only 'stopping the heart' will be enough, then his ablity stop
for machine maybe, destroyed, or it's permanently deactivated
for magic, cut off the source of magic power, or simply vanished/destroyed
what if he kill attribute? like fire, or even space?.. well i cant imagine it
So his abiliy is to apply all that can be considered as dying to his subject
That’s why he can kill ice.. or basically anything
conclusion : his ability is op as hell!