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.
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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 labor; 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.