Not every rock can be broken to create a good cutting edge, but most parts of the globe have abundant rocks that will work. Some of the best choices for cutting stones are flint, chert, jasper, chalcedony, quartz and obsidian. That last one is a form of volcanic glass common on the west coast, which is capable of being broken into such sharp pieces that the cutting edge can be just one molecule thick in some spots. That's 25-times sharper than scalpels used in modern surgery! So put away any ideas that rock won't cut.