I cut fabric all the time on mine. I use Heat and Bond lite. I do not use the same mat for paper as I do for fabric. I use the deep cut blades. I do not use the same blades for paper as I do fabric. They are labeled and placed in a separate container so I don't mix them up.
Starch your fabric. Cut the fabric the same size as the mat. Iron the wrong side of the fabric to the Heat and Bond. Do not peel the paper off. Place the fabric side down onto the mat and using the scraper smooth out the fabric so there are no air bubbles and fabric/Heat and Bond is completed adhered to the mat. Set the speed to the fastest speed or just below. Find your design and cut. The Heat and Bond Lite is sewable. I have also used mats that are not that sticky after some use. I then use painters tape to secure the prepared fabric on all four sides to the mat. When the blade appears to be dulling, I put that blade in my paper blades container and put on a new one. I cut quite a bit of fabric appliques before I need to put in a new blade. My sister also does this and never has issues either.