When building box stalls I needed to cut /trim floor matts.
Tried all kinds of saws, friction blades oil etc.
They would however create a smoke screen from burnt rubber.
Finally came up with a plan.
I would flop the floor matt over a 4 x 4 and using a new box blade c/w a straight edge make a cut (deep slit)
Being over the 4 x 4 a hump was formed allowing the slit to spread open and that reduced friction.
Usually 2-3 box blade passes and the 3/4 " matt was neatly cut where I wanted.
Also discovered that dish detergent sprayed in the cut zone acted like a lubricant while oils did not help.