Self healing cutting mats are good - avoid making deep cuts, as the mat won't heal. When trimming prints face down, I have a sheet of tissue under the print, for protection, and it helps with rag papers to prevent the very edge of the print from "bedding down" into the cut.
A couple of years ago, a neighbouring business dumped a glass display cabinet in the street, from which I took three 24x36" shelves - about 10mm thick. These are great for cutting on, and I have no fear of handling them, as they are made from strengthened glass, and have rounded edges. I'll sometimes use a lightbox under the glass, to align prints to the substrate.
My main cutting table has 8x4 sheets of polypropylene as a cutting surface - was used by a supplier as packaging for a delivery of DiBond on an open wagon. Two sheets have lasted for about four years! Also have a table with a 2x1m self healing mat, and various smaller matts which get used when it's easier to rotate the cutting surface, and keep the print in one place.
Pretty much all cuts against a mat are made using 10A scalpel blades (a couple of hundred per month!).
One day, I'll make a back lit 8x4' cutting table with a glass top...