I use the variable speed Dremel and have no problem cutting carbons. One thing that I found I have to do is first cut off an inch or two from the arrow before making my final cut. This is because the cutting disc is not very large and the Dremel unit itself can get in the way when there is too much shaft sticking out.

I turn my Dremel up all the way and never had a problem with melting. I've used this method on everything from carbon Express to Eastons.