A device for cutting, using laser beams (B1, B2), a material (A) such as a material for manufacturing sanitary products comprises a supporting formation for the material (A), such as a motor-driven belt, including a net (72) for supporting said material (A) in a position corresponding to the area of cutting where the laser beam (B1, B2) acts. Typically said net is a wire net, e.g., made of steel, bronze or a combination of the two, to which there is preferentially associated a rotary cleaning brushes (9) and suction and/or air jets systems.