Well not exactly.
I was a gem cutter for years before I became a goldsmith.
Gem cutters will never get away from that old 1972 Mercury Marquis Brougham commercial where an old Jewish master diamond cutter cleaves a large rough diamond in the back seat of a car. Everyone thinks it was a Lincoln Continental, but it was not. His comment, "If it goes right I have a $150,000 diamond ... if not, dust!" is all baloney. It might not cleave at all, or cleave at a different angle, but it won't shatter into dust.
SNL did a great spoof of that commercial with a Rabbi doing a bris in the back seat ... "Poifect!"
The steel wedge is placed in a groove sawn in the diamond crystal with a diamond saw on one of the cleavage planes. The wedge is placed in the groove and struck with a mallet creating a shock wave that causes a crack to propagate along the cleavage plane ... and split the diamond. Pretty much the same principle as a stress riser on a knife blade. Cleaving is only used on large rough to make more than one finished faceted diamond. A large rough crystal may be cleaved into three or more pieces. While some crystals are sawn to rough shape, most diamond crystals are shaped by abrasion on large iron laps charged with bort (tiny diamond crystals). This roughing to shape is called bruting. After bruting, they are faceted with finer diamond powder.
Diamonds will abrade diamonds because there are different planes in the crystal structure. The cubic structure of carbon creates the octahedron diamond shaped crystals, which have flats and corners. The corners of the crystal are slightly harder than flat surfaces. Thus, the corners of the bort wear the flats of the stone being cut. This is where a diamond cutter has to study the crystal and plan on what shape he wants to cut and how to orient the crystal on the lap.
Now days they use lasers to cut and shape the rough and computer operated faceting machines that resemble modern multi-head milling machines. These machines can cut diamonds from, 1/400th a carat to any size or shape the rough allows.
Cutting all other gemstones is simpler. The laps are either coated with sintered diamond, or charged with bort. Polishing is done with very fine diamond powder or other hard metal-oxides.
I found the SNL clip. I guarantee it will make you laugh.