Thanks for all the feedback so far. I don't have a band saw (still trying to find a deal on CL), so that's out of the question. I've thought about using a miter saw, but I feel like it would just burn the paper since I would have to go slowly (maybe not? I don't know; also considered the table saw; same concern). And as for a jig saw, I don't think I've ever seen a 6" long fine tooth blade. I think that would be the minimum needed to clear the roll and taking into out the reciprocating action.
I do agree on never using the red rosin paper, which is why I got the brown rosin paper from Lowe's. I read a lot about the bleeding problem, so that made my choice a little easier.