No, it doesn't hurt the die. The cutting mats are 'consumables' in other words, you will have to replace them, just like you have to replace your rotary cutter blades. You can extend the life of your mat by changing it's position on the die, flipping it end for end and using both sides. They also come in different sizes, so if you find you are always just using a portion of a die, either position the mat as Onebyone suggested, or get a smaller mat for when you just cut this shape.