Hello there! This has come up in the forums several times - HERE
is a recent conversation that has a couple of other links mentioned as well. The issue is usually a little too much pressure from the machine, pressing the edge of the die into the paper as well as the cutting lines. I would try the suggestion of running the cut piece back through the machine without the die, or using a bone folder to smooth the edges down. If you're able to adjust the thickness of your sandwich using shims instead of one of the plates, that should help to reduce the pressure too.