Having working in Asphalt plants most of my working life cutting/repairing conveyor belts and we also have horses, so we have those several of mats around here too.There is a way to cut rubber, be it conveyor belt or the stall mats. Use a new utility blade, use a thin straight edge, something like a square or a 1/8" flat bar aluminum from home depot. You want it thin to keep the knife 90 deg. to the mat. Something thicker like a board or level pushes the knife blade at a angle because of the thickness of the handle and rides against the edge instead of the blade. Since you want small squares, start with making long strips first. With the straight edge on your mark and holding it firmly down make a couple cuts, always in the same cut with some pressure, don't try and go all the way thru. Now that you have a couple cuts started, take a 2x4 and slide it under the cut off to the side a inch or so. This will open up the cut. You can cut the rest free hand if you think your steady enough or just keep using your straight edge. Don't pull towards your body, stay off to the side of your knife, think stored energy if your knife should slip out from the cut as you pull. It's not hard or a one cut and done either. Just get those first cuts started to open the cut and you'll have a much easier time,,,gregg