When cutting any thick industrial grade of dark (carbon black infused) rubber (ie tyre rubber but up to 5-20 times thicker), always use a very sharp butchers knife approximately 10-16 inches long, a mixture of 40% cheap hand or dish washing soap and the rest water. Do not blend the two liquids too much. If it froths, it's no good.
Start the cut until you can fit a small pinch/crowbar behind the blade, then gradually lift out on the bar while slicing at a slight angle which seems counter-intuitive but actually will plumb it close to 90 degrees.
Constantly dip the blade in the aforementioned solution, and if the rubber is bigger than 80 mm's thick, switch to a long crow bar. If you're on your own.
Never use a mechanical saw or power tool on any rubber unless you want to be decapitated, lose a limb, or genitals.
There are exceptions to this rule but I don't want to be responsible for any unsupervised tomfoolery. Stick to long thick stainless steel butcher knives, the solution, and an adequate prying device with a steady motion (at an angle once started).