You won't damage the straps, but they will start to fray like a cat pulling on a ball of yarn. If you're going to cut the straps, tape the ends or try some heat shrink over the ends.
I haven't cut the excess strap material on mine. But wouldn't a "hot knife" work. I beeelieve the material is a nylon base. If so heat up an old kitchen knife either on the stove or with a propane torch. Then use it to cut the surplus material. The heat will cauterize (sic) the ends so they don't fray as the blade melts through the material.
I use this technique on nylon climbing ropes and harness material. Its worked very well for me. Anyway just a thought.