Yes, you can break rock with a jackhammer. Jackhammers are designed to break through concrete, asphalt and other hard materials. The blunt force of the hammer head breaking through the material is what causes the rock to break.
If you're trying to break up a small piece of rock, you may be able to do it by hand. However, if you're dealing with a larger piece or multiple pieces, you'll need to use a jackhammer. Start by setting the point of the chisel on the rock and then striking it with the hammer until the rock breaks.