In your profile I see a laser diode machine.
If this is the machine you want to do all the work with, take into consideration what @jkwilborn started saying.
I have to cut the plexiglass with a router and then not do the engraving. In my case, I don’t want any paint to remain, so I used tempera paint, which comes off simply with tap water.
If you want the paint to stay, I use another type of paint for that purpose.
If I had a machine capable of cutting plexiglass, after doing material tests to evaluate the ideal cutting and engraving settings, I would paint the plexiglass, engrave it with the ideal settings obtained on painted plexiglass, and finally cut it.
Here I leave my “journey” about my learning with polystyrene, which is identical to plexiglass.