Those suggesting a utility knife must be cutting some kind of horse stall mat that I'm not used to. The one's we use are made from recycled tires. No way in heck that a utility knife, even in the hands or Arnold, could cut through them.
I mark with a silver sharpie and a straight edge, put a pair of 4x4s under the mat parallel with the cut, and use a medium-fine blade SawZall, relatively slow speed.
I've tried lubing and not lubing the blades. Doesn't seem to make a whole lot of difference to the cut or the blade. The lube comes off as soon as the hot rubber melts on the blade. I prefer not to get a bunch of petroleum on the mat, as the horse will be eating off of it later. WD40, mineral spirits, acetone, alcohol, wax and grease remover (nearly anything) on the blade AFTER the cut and the rubber comes off.
I cut 3" holes near the edges with a hole saw. Makes man handling those heavy bastards easier when I need to move or remove them later.
Lump