I just cut mine when finished, and hold the starting threads nice and firmly out the back of the machine. You can see where I've been lazy and haven't held them because the machine pulls one in and I get a loop underneath at the start.
I used to perforate the paper before starting too... sewing along the lines with no thread in the machine. But since I started using a much smaller stitch length I haven't bothered and I'm finding it just as easy to get the paper off.