I've not used fleece for a backing, but perhaps the rubber sheets that are used for cabinet drawers and shelves would work if you have a roll and lay it under the fleece so it will adhere some, then try cutting. I don't know if that will work or not, but I know that these rolls work for lots of things and work well under the sewing machine to keep it from walking when you have to sew on a table. The owner of Jordan fabrics used hand weights that she lays on the end of her ruler when she I cutting to keep the ruler from moving, this might help with the fleece I you have some of the hand weights and place them near he edge of the fleece worth a try.