Remove the steel belt from the tires using a reciprocating saw or dremel and a chisel. Cut the sidewall out of the tire with a utility knife. Wear heavy leather gloves to protect your hands from the sharp blades.
Rent an industrial shredder. Before renting, check with the rental firm that the machine is approved for use on tires.
Cut the tires into pieces small enough to fit into the shredder. Insert them into the shredder according to the machine's directions.
Use a serrated knife to cut up your tires if you do not have access to a shredder. The pieces should be about 1 inch square. This is a tedious process, and you will need to sharpen your blade frequently.
Apply the mulch to your garden. Because the rubber is so dense, it should be applied at half the depth of wood mulch.