Can a diode laser cut or engrave acrylic? What colors, thicknesses, and techniques work best?

In the visible spectrum, the further a color is from blue, the easier it is to cut and engrave. Blue, purple, and green are the most difficult to process, while red and orange are easier. Note that opaque black acrylic cuts best of all colors.

The above assumes the acrylic is not translucent. If it is translucent acrylic, it is almost impossible to cut regardless of the color, because most of the laser energy will pass directly through the material.

You can try it out, and if you find you really enjoy this hobby, you can save up for a CO2 laser cutter, which can effectively cut and engrave various acrylic materials, and almost all organic materials.

Alternatively, you could try using a UV laser, if you have the budget to buy one. UV lasers work very well for engraving and cutting acrylic (including clear acrylic). I use an F2U UV laser, and it works great.