John
Just use your table saw.
In the machine shop we routinely cut 1/8" thick plexi with it and have no problems with it making a mess. It can leave a pretty rough and sharp edge, so just make sure to hit it with some sandpaper to take away some of the burrs.
If you have a dremel, depending on the length you are cutting, you can use a router bit with it.
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Here's another easy alternative for you if you can't get the plexi to work.
Ge a package of the "reinforcemants" for when you put binder holes in a piece of paper, and put rings through them on your individual car cards. Hang a few eyehooks around the layout to hang hte rings on and you're all set.
I happen to like the ring / hook type better, simply because the cards don't end up in one giant pile if you space the hooks out.
Well I used a combination of materials I had laying around.
I used the table saw to cut the plexi. I think the key to a clean cut was to set the blade low enough to barely go through complettely. I like the results. I left the ends open as I would think it would be nice to move the cards through the side when you cannot get a hold on them.