As a suggestion when cutting plexiglass I would cover both sides with masking tape, to keep the cut shavings from melting back. Then, cover the surfaces with thin cardboard and tape it in place. Attach the pattern to the cardboard.
When cutting, use a slow speed to reduce the heat generated. I would use a 2/0 reverse-tooth blade and a metal cabinet scraper to clean up any rough edges. For a frosted look, 220 grit paper should do the trick.
This same process could be applied when cutting vinyl records.
Will be trying this process to vinyl records in the New Year.