LBD, yours looks like a CO2 laser?
That's an important piece of clarification... Most diode lasers will need something additional as a backer or substrate to cut/etc clear acrylic, like Kenny said. But CO2 lasers can do it fine. Of note, cast acrylic will do better than extruded
Also, be sure you understand the safety aspects of a laser when it comes to their fumes, especially with acrylic.