A device for cutting a web of material

A device for cutting a web (2) of material comprises movement means (3) for moving a web (2) of material to be cut, defining a feed path (P) for the web (2) at least partly rotatable about a central axis (A) and equipped with at least one conveyor (4) mounted around the central axis (A), at least one cutting head (7) equipped with a laser source (7a) and an optical system (7b) configured to direct the laser beam (F) towards a cutting zone (Z), where the optical system (7b) of the cutting head (7) comprises at least one directing member (8) located inside the conveyor (4) to direct the laser beam (F) away from the central axis (A) towards the cutting zone (Z).