David, Most plastic slates are made of materials that will crack readilly. so I'd reccommend the drill and file technique rather than any kind of punch you'd strike. Don't forget to back the piece with wood when drilling. Drill 1/8Th in ch holes as close to the ends of the proposed slot as you can, then you could drill out some holes in the middle to make cleanout easier.
You could try cleaning up the edges with a wood chisel held vertically with the flat sides out, but either press only or tap very gently to avoid cracking. then file it clean. tom Fowle
