To do this we use a tool called a swivel knife. As the name implies, the knife is made so that it can twist or swivel as it's cutting through the leather. By taking advantage of this the leatherworker can cut clean curves into the leather and isn't restricted to straight angles. Cutting the grain of the leather (the smooth, strong top side) makes a clean border in the surface of the leather that the rest of the carving is built on.
The swivel knife needs to be kept razor sharp in order to cleanly cut the leather so every few minutes it gets passed over a strop of some sort. Sometimes it's a peice of scrap leather but I find a bit of scrap brown paper seems to work better. Whatever I use, it's liberally treated with jeweller's rouge which is a sharpening agent. Any of the microscopic imperfections that are dulling the edge get whisked away by the rouge.
Due to subtleties in the leather and the fact that all this is done by hand it's virtually impossible to cut any design exactly the same way twice. Accordingly every piece comes out just a little different from the others guaranteeing a unique product in the end.