Diamonds are cut to shape using a variety of techniques. The oldest method is cleaving (breaking). Diamonds have very predictable cleavage, and a skilled cutter can break the stone with great precision. This method is still used to separate high-value rough into multiple stones. There is no waste with this method, but you are limited to the direction the stone will cleave. Most rough now sawn. The saws are small circular blades (.004" kerf) with diamonds embedded in the rim. This process is good for mechanized, high-volume, gem cutting. Saws are limited to cutting in certain crystallographic directions, diamond harness varies according to orientation of the crystal lattice. The newest method is laser cutting. Lasers burn through, the crystal and can cut in any direction. The kerf is thicker with lasers, but they can be used on less than perfect rough. There's also a chemical diffusion process, but it is very specialized and I can't remember the specifics. Final shaping and polishing is done on a spinning cast-iron lap embedded with diamond powder.
Diamonds have very high wear-resistance, but are prone to chipping (it happens on wedding rings all the time). I would also guess, that due to the blocky crystal lattice, you would not be able to get diamond as sharp on a molecular level as other crystalline materials.
Phillip