Plexiglass is best cut with a draw knife, also called a hook or scribe knife, or plexiglass cutter. This hook knife will score the plexiglass, and remove a wide, shallow line after each draw pass so the plexiglass may be snapped off.
Using power saws to cut the Plexiglass usually melts the plastic because of heat generated by the moving blade. If the blade is too fine or the plexiglass is moving too slow, it could melt from the friction. Then the melting plastic sticks together behind the cut leaving a mess.
To cut a straight line, the hook knife is the best. This draw knife works best with a straight edge to guide the scribe knife to cut a grooved line so the plexiglass will break along a clean fracture.
To use the plexiglass cutter, the first pass should be shallow and easy. The following couple of passes should be deeper and straight, pushing harder with each pass.
Some people will use a utility knife. It is more difficult because it meanders on the plexiglass surface. It can work, but not as well as a hook knife.
As to power saws, a circular saw, saber saw, or table saw may melt the plastic.
If you must cut a curved line, a dremel grinder or oscillating tool may be an option. A jigsaw may work, but melting is still a problem.