I had the same problem, so temporarily abandoned my project. However, I think the way to avoid this is to buy some cheap coffee filters. Place one on top of the die before positioning your fabric. When you run the die through, it cuts both the paper and fabric but the paper stops all those threads from sticking in the dye. You can use just about any kind of paper, including typing paper, but I think coffee filters are the cheapest and easiest to obtain.