This is the way I would do it. "I" should be boldened, but I can't do it here. Because it is the right way to do it.
Get a metal straight edge. Get a razor cutter (not a box cutter, but like a Stanley sliding blade), and a couple of clamps. Put the plastic on something slightly rounded, like maybe a thin strip of carpet under a wider one. Clamp the metal along the line. Cut easily, the object is NOT to cut all the way through, but make several repetitive progressively deep cuts. The hump under the carpet should be placed under the edge of the cut so there is a slight crowning. This lets the "drop" drop, and opens the cut into a V so the next progressive cut doesn't bind along the way and to astray.
I have cut 3' wide 1/2" thick layered rubber conveyor belt material with this in less than a minute once the clamps are set up. DON'T USE A LOT OF PRESSURE, YOU WANT TO MAKE A SERIES OF PROGRESSIVELY DEEPER CUTS until you're through the material. Don't get in a hurry. Take your time, and you'll come up with a very clean cut. If you want to bevel it slightly, tilt the blade a little. Works on luan, and other materials, too, and gives a straight clean cut.
HTH.
Steve