As @JohnJohn points out, a diode laser is the wrong hammer for clear plastic, because very little of the energy gets absorbed.
I assume you want to cut out the window pane to install in a sash.
I recently had great success making perfectly rectangular holes in paper with a CO₂ laser by “engraving” them hard enough to vaporize the paper, rather than trying to “cut” them:
Perhaps “engraving” a small rectangular border around the window pane, with a very thin paper overlay to absorb the energy and transfer it to the plastic, will do something either useful or interesting.