While building your own professional-quality tire cutting machine is near impossible, a professional machine isn't the only way to cut tires. You can either recycle your cut tires or get creative and use the cuttings for something like sandals or planters.
You can cut tires using a sharp blade, such as a utility knife or box cutter. While this method is the cheapest, it also involves the most labour; manually cutting through tires requires patience, carefulness, stamina and strength.
A wood chisel may make the job easier than a blade. After cutting a small opening to insert the chisel, you can begin cutting away at the tire from the inside by placing it over a piece of wood and cutting through with the chisel's sharp edge.
The easiest method is to use a band saw. These saws easily cut through the tire and allow for angled cuts. Like the chisel method, you'll need to cut a hole in the tire first to give the saw blade a starting point. While circular saws work well, too, they cause smoke that makes it harder to see, a huge safety risk.