Are you piecing the borders or cutting a piece that is one long length of fabric? I have folded up to 4 layers and cut very carefully without problems, but 2 layers is much better. You would have to move your cutting mat as you went along and check your layers to be sure that they have not moved. It would almost be easier to cut 40 inch sections crosswise and sew them together. It may depend on the pattern in your fabric as to whether you would want to do that.
Beth