I generally cut any synthetic line with an attachment to a heavy duty pistol grip soldering iron. It's about a 2 inch long blade, which melts through the line, fusing the ends as it goes.

I bought it at a marine supply store on the waterfront, but, if I see it online somewhere, I'll post it. I bought it when I was making up a bunch of mooring lines, using 5/8 inch braided nylon. The "blade" is really just a flat plate about 2" x 3/8". When you heat it, it goes through the syntheric line like a hot knife through butter. You can even use the flat part of the blade to taper the end of the cut so it will pass through things better. I'll try to find a pointer to it somewhere online.