A food grinding machine comprises a static outer jacket provided with conventional elements for coupling to a loading inlet of the grinding machine. Annular recesses are formed in the internal thickness of the jacket, have preset volumes and are mutually separated. A food pusher and cutter element is mounted inside the jacket so that it rotates coaxially, and a screening element with differentiated passage regions is interpose between the pusher and the jacket. Each region can be crossed at the annular recesses.