I've used all kinds of things to cut Plexi... but the key things to remember are: USE SOMETHING WITH FINE TEETH AND USE TAPE. (but don't use the tape on the painted side, you'll probably pull the painting/printing off)
Put the tape down, draw your line, and cut. Don't use some 4 to 5 teeth per inch blade, you will destroy the marquee. Use a piece of something under it to support it... and something like a clamp to hold the marquee. When I'm using a power saw, I like to put a piece of scrap material under it so the blade has something to hit under it. You DO NOT want to hold this thing in your hands if you are cutting it with a circular saw and a plywood blade. You are too close to the blade. Power miter or cut-off saws can do well with plywood blades. Avoid Jigsaws as the up/down blade motion tends to case plexiglass to shatter as the blade binds and slaps the plastic against the guard.
Sometimes you can do a score & snap method, but that doesn't work too well with taking off such small amounts.
Also, if you have a fine tooth blade or a cut-off disk, you can use a dremel too to cut it. It will basically spin so fast that it melts the plexi and leave a bunch of crud on the edges of the cut but that just snaps right off with your fingernails. I wouldn't recommed this on a cut edge that will be seen. If it is hidden under where the marquee mounts, it will work fine.
Now, if it's glass... You can score it with a glass cutter, heat (not too much tho!) the cut on the UNPAINTED side with a torch, and hit it with cold water to crack it right down the score line. That's kinda like the old days with the Ronco glass-o-matic where you could turn soda bottles into drinking glasses. (I guess I'm showing my age there)
RJ