I was in the plastics industry for 7 years as branch manager of a plastics distributor including ICI perspex and we regularly cut and formed actrylic and many other semi finished plastics for point of display customers, signmakers and engineering companies etc. Needless to say, I have a lot of scraps and offcuts still which are of great use :wink:
There are a number of ways to cut it but it depends on the thickness of the acrylic. I personally wouldn't use water as that was not an advised method in my day though things may well have changed.
First - how do you know it's "plexiglas"? There are several other plastics it could be clear ABS, polycarbonate, polystyrene or pvc for example and all have different properties and cut slightly differently. Some are soft, others very brittle.
If very thin it's possible to score and cut but if you have limited tools then the advice to drill small holes all around is good, you can then carefully file it clean.
You could buy a 120mm hole cutter for about £10 - 15 or a really cheap set and use on slow speed drill (whatever you do put a flat bit of chipboard or similar under for support or it can crack.
You can definately cut with a jigsaw but only if a variable speed model and on slow speed (I've done it many times) but best to support and cut through the support as well. I use a fine blade BTW as coarse can chip and crack the plastic.
A scroll saw works beautifully
An expanding wood bit also - slow and careful. Ideally cut part way then turn over and cut from the other side as well.
If you break it, providing it's flat sheet then it's not expensive to replace.
As an aside - make sure you wear safety specs as the swarf will be statically charged, will stick to everything and will be sharp. Not advisable to get some in your eyes.
Just the benefit of my experience - others will do it differently and it's 2o years since I was in the business.
cheers
Bob