Machines and methods for cutting products. Such a machine includes an annular-shaped cutting head and at least one knife that is oriented axially at an inner circumference of the cutting head and extends radially inward into an interior of the cutting head. An impeller is coaxially mounted within the cutting head and has a base, a ring spaced axially from the base, an entrance to an interior of the impeller defined by the ring, and a unit for delivering products within the interior of the impeller toward the inner circumference of the cutting head as the impeller rotates within the cutting head. The delivering unit includes paddles that are circumferentially spaced within the interior of the impeller between the base and the ring. The outer circumference of the impeller has a diameter of greater than 35 centimeters.
