The main use of cleaving is to…well, cleave. One solid chop through a dense piece of meat or bone. Use a one-handed grip and hold the food you’re cutting down with your hand in a fist a good way away from the cutting area. This keeps your digits away from the blade and attached to your hand.
Gripping the handle tightly with your other hand, swing it down in a forceful but controlled strike, never taking your eyes off of your intended target. You’re going to hit what you’re looking at, so do NOT look at your other hand during your swing. For safety, don’t raise the cleaver above the head or chest level. The higher you go, the more things there are that can go wrong. If a basic hammer swing doesn’t do the trick, you probably need a bone saw.