I would think you could cut it pretty easily with real tools. I would probably put a line of blue tape on it, just like you do when you cut through finish surfaces and cut through that,
I know when I have mats break (and they aren't the type you have) sometimes the edges remain rather sharp and sometimes you can get some nasty sliver pieces break off. Again, you can tape that over for a smooth edge. Maybe lightly sand?
But for many years I kept a terrible awful coffee table of fake wood and glass inserts because it was just the exactly perfect size to fit an Olfa mat and there was just enough lip of fake wood left to keep the mat in place plus it was a good height so although my posture was terrible I could sit on the couch and lean over and do my cutting relatively easily.,,