As you have already found out, cutting P-glass is tricky. The plastic cutters you mentioned are very gimmicky and don't work that well. I would suggest the following procedure:
After marking out your cut on the plexi, take a scrap piece of any firm material, plywood, an old board, anything, and cut a slightly oversuninstallized hole in it to act as a backer for your plexi.
With your plexi on top of the backer, Drill holes in two oposite corners of the marked hole you want to make.
Use a varible speed jig saw at a very low speed with a fine tooth wood or course tooth metal blade to cut out the shape. Stay just barely inside of the waste side of the mark.
Finish the hole and smooth the edges with a fine bastard file and some 220 grit paper.
If you are really cleaver, you could make the hole smaller than the device cover so no plexi edges would be exposed. You may need longer screws to attach the cover plates, but you can get them at any electrical dept.
Until you get to very thick small units, or goods more rigid than plexi (such as glass, which also flexes and sags) you will have some deflection. It also depends on whether there will be any weight on it.
If 1/4 inch (with no load) is not a problem (this is a guess) then you may be ok. If you are putting a 10 lb. plaster statue on it, it will flex. If it can't flex more than .001 inch, no matter what, it won't work.
It also depends on how you affix the edges. The more captured they are, the less flex. Touching the middle of a 3x3 acrylic sheet, less than 1/4 inch thick, that is not tightly locked around the edges, will likely flex significantly.
Manufacturers may offer specs on how much their plastic flexes over certain distances.
Best Answer
A drill bit will cut holes in acrylic, but don’t use acrylic or you will probably experience breakage like your example. Use polycarbonate, a name brand is Lexan. It can be purchased in the same thickness. It is usually a bit more expensive but it will not crack even when dropped, or hit with a hammer but will preform exactly the same otherwise.