Plexiglass and acrylic are easily cut with a draw knife, called a hook or scribe knife, or plexiglass cutter. This draw knife strips a layer of the acrylic with each draw pass so the plexiglass may be snapped.
A draw knife scribes or removes a groove in the material weakening it thus allowing it to ‘break’ along that line as opposed to using a utility knife that only cuts into the material. The utility knife does not remove material like a draw knife and so it takes many more cuts into the material to achieve a weak enough trough to achieve a clean break.
Usually 3 passes with the knife is sufficient to ‘break’ the plastic along the scribe. Most plastics cut similar to wood and so I have used all my woodworking tools to cut Plexiglas at one time or another.
Using a power saw to cut plexiglass will probably melt the plastic due to heat from the hot blade and friction.
Cutting straight lines with the hook knife is easy and quick with a straight edge to guide the scribe knife to snap cleanly.
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. A utility knife won’t cut as the blade will wander along the plexiglass surface.
To cut a curved line, dremel grinders or oscillating tools work okay. With a jigsaw blade melting is still a problem.