What size is the square you have to cut out? There are some standard-sized acrylic squares available at JoAnn's. If it's not a standard size, you should be able to take it to a hardware store and have a piece of acrylic cut to the correct size (bring the template with you). I haven't done that, but I know there are some quilters who do. I'd probably put some sandpaper or clear grips on the bottom of the template so it wouldn't slide around. With that many pieces to cut out, I might also consider getting one of those little cutting turntables. I'd also layer the pieces to be cut, maybe 2 to 4 at a time.
HTH!