A device for cutting a web of fibrous material including movement means for moving a web of fibrous material to be cut, defining a feed surface for the web and having at least one first cutting zone, at least one laser source configured to generate a laser beam extending along its operating direction towards the first cutting zone to make, on the web, at least one incision extending along a predetermined cutting line, where a portion of the laser beam passes through the web of fibrous material at the first cutting zone. The device also includes recovery means for recovering the portion of the laser beam and at least partly located along the operating direction, at the first cutting zone, in such a way as to intercept the portion of the laser beam and direct it towards a second cutting zone to make a further incision or cut.
