It’s not exactly wood but, it’s a troublesome material with regard to odd flammability:
Some time back, I tried cutting some amate bark paper. It acted like incense. The laser would touch off a glow along the edge that would slowly consume the paper, converting it to ash. I tried wetting it before cutting and, that stopped the burning but, the wet paper was very fragile and it deformed a lot as it dried. It could likely be weighted while it dries to compensate but, I decided it was too much hassle at the time.