Eric,
Acrylic and polycarbonate can easily be machined.
Keep the feeds and speeds fairly low, otherwise you will melt the material rather than cut.
If possible, use razor sharp new tooling for the job. I do a fair amount of it, and if you are careful, with a soft buff and a very fine polishing compound the edges can be brought back to a perfect finish. Again, you have to be very careful not to heat up the edges, otherwise they will burn and 'string'. You can polish back by hand using the finer grades of metal or silver polishes and soft cloth (old t-shirt).
The way commercial people get the smooth edge and shine back is either with a flame, or chemically, by feeding the edges thru the fumes of certain chemicals, of which I have know idea which ones they use.
John