I just cut 1/4" today. I needed strips 1/4" wide to end up with 1/4" by 1/4" by 48". I did it with a fine, but not the finest jig saw blade. Keep in mind that a jig saw blade will not give you a straight line no matter how hard you try.
For cuts that need a straight line, I used a hand saw with a tall, straight, wide blade with med to fine teeth. I drew a line with a sharpie, and after 48", you couldn't see any ink on either side of the cut. It stayed perfectly straight/true. That plexi was only 1/8", though.
I've heard that you can use a circular saw. If you do, set it to the minimum blade depth required.
Some things to look out for:
As you cut the plexi, it can re-weld behind the blade. Try to go slowly.
Secure it down near the blade so it won't bounce and crack. The melted plastic likes to grab the blade.
Good Luck.