I had similar thoughts because you’d have to overpower the cuts.
That being said, I find that I always cut 2 layers. It prevents smoke marks on the bottom of the top layer (which is the one I want). If you have the right kind of paper surface, you could mask it, but I find that a waste piece of cardstock underneath does the job really well. I just finished a cardstock mask, it was essential to prevent smoke marks and char because the bottom surface is the outside of the mask.