You can easily cut carbon shafts with a Dremmel tool and a cut-off disk. The problem is getting a right angle cut. You should be able to work something out by mounting the Dremmel on a 6"X3'X1" board, and working out some kind of bracket to hold the nock end. Of course it's a lot easier, though more expensive, to just buy a carbon arrow cut-off tool, which is easily adjustable for whatever length of arrow,you want.
On any kind of tool, rotate the shaft into the cutting disk rather than just pushing it to maintain as much of a 90* cut as possible.