I'm really surprised that you are making them. I assume they are for watch cases. But aren't you aware that you can order virtually any shape or size of plexiglass watch crystal from G & S? Here's their website.
They also offer flat perplex (the commercial name of the plastic used in watch crystals is "Hessalite") if you want to cut them yourself.
If you are frequently cutting out various shapes that are geometrical, then all you need is a miniature table saw equipped with a plexiglass cutting blade. This is ideal for cutting squares and rectangles.These are very small miniature units for model ship makers. The German firm Proxxon makes a well known miniature table saw. But if you have a regular table saw, you can do it on that too with a plexiglass blade.
If you are cutting irregular shapes, then a jigsaw with a plexiglass blade is just the thing for you. For rounds, you can buy all you need from G & S very cheaply. If you are in Europe, contact Rpbur in France or Sternkreuze in Germany.
But if you have to make a lot of them, stop using your precious time on something you can buy for a few dollars from G & S.