A mill for shredding scrap, comprising a shredding chamber able to contain scrap during the shredding and having a shredding unit, an inlet pipe connected to an opening of the shredding chamber, in order to transfer the scrap toward the shredding chamber. The mill comprises first thrust means associated with the inlet pipe, selectively movable between a loading position of the scrap into the inlet pipe and one or more intermediate positions to transfer by means of thrusting the scrap toward the shredding chamber. The mill also comprises second thrust means, disposed in proximity with the inlet of the shredding chamber, selectively movable between an inactive position, in which they do not interfere with the introduction of the scrap into the shredding chamber by the first thrust means, and one or more thrust positions in which they introduce into the shredding chamber the scrap moved by the first thrust means until the scrap is in proximity with the opening.