I’d remove the masking from the side facing the laser. Do not mask this face (mirror acrylic only).
Remove the down-face masking before cutting, and either replace in selective areas with masking paper, or place a manilla folder (open) beneath the down-face and the bed. The extra thickness won’t affect your outcome, but will make finishing small pieces much easier.
If you don’t already do this, start having a piece of tape handy at the end of the cuts. Use the sticky side to lift pieces while you press the board down (don’t move side-side). If anything does not release, then leave in place and cut again.