I wouldn’t recommend actually doing this yourself, but as a test I have cut through 1/4" plywood. Laser cutting is material dependent. Here’s a good list of materials that can be cut / engraved:
This laser is 450nm wavelength (a blue laser diode). 450nm wavelength energy is readily absorbed by organics like leather, wood, etc. But inorganics like glue do not readily absorb the energy. What this manifests as is solid wood cuts well, but MDF, plywood, and other composites that have significant amounts of glue struggle moreso and require slower feed rates and more passes with smaller Z height changes. Additionally the thickness of the material matters a lot, with thicker materials not performing well.
For example, 3mm plywood can be cut in 4 passes, but the 6mm plywood I tested required 50 passes. MDF, being significant amounts of glue holding the paper fibers together, cannot be cut reliably at all, except maybe the thinnest amounts.
Corrugated cardboard and grayboard have significant adhesive in their composition, but corrugated is quite thin sheets of paper whereas grayboard is thicker.
CO2 based lasers are popular in part because the laser is extremely short wavelength and can ablate even inorganics, leading to fast cutting.
Diode lasers are better for engraving as they darken wood nicely and evenly. Laser engraved designs on wood cannot be done with CO2 lasers and it doesn’t brown wood, it ablates to different depths depending on power.
If you are primarily looking to cut thick materials then a weak diode laser is not a good fit, and a 40W CO2 laser would be more appropriate. Unfortunately they are also very expensive.
With diode lasers, after a certain thickness it’s usually better to CNC cut the part, leaving a few holding tabs on, then replace the toolhead and finish engraving the design with the laser, if you so choose.