Take an animal and lead it, then stick the lead to a post enough high that the animal doesnt touch the floor, wait some time (40s/1min) and then cut lead.

Animal released from lead will take damage as it had fall from a big pit, and die.

Steps:
1. Make a tall fence, 9-10 blocks high.
2. Stick the mob to the highest part of that fence, so it will not touch the ground.
3. Wait some time....
4. Release the lead, animal will die.

The more time in air, more damage will get when hit ground....