The trick seems go be getting a good feed speed.
My bike has a 1/4" thick screen, and I'm not tall, so I decided to take about 2" off the top. I marked it and got out a new jigsaw blade. Concentrating on the curve (and it's not flat either) I didn't go fast enough and, to my chagrin, the cut closed up behind the blade, as I was scuffing and melting rather than cutting it. I also think the blade was too fine - the woody rule about three teeth in the cut doesn't seem to apply.
Since then, I've had excellent results on bandsaw, tablesaw and even mitre saw, but in each case being sure to go fast enough and to arrange really good chip clearance. On the mitre saw the stuff gets everywhere, as it's fluffy, not at all dense and statically charged by the cutting process.