Most 2mm wood should be cuttable. You will need a lot of experimentation to find the best settings for your particular wood, and you’ll likely need 10+ passes.
A quick dig through the forum finds these threads:
So the absolute record for laser-cut wood thickness with a Snapmaker2 seems to be @brent113 and his 1/4" (6mm) plywood in 50 passes.
I’d probably try to find something in 1/16" (~1.5mm) unless I really needed the thicker stock.