An apparatus for cutting cuttable pieces, especially of animal or vegetal origin, into prismatic, preferably cubical shape, includes two concentric knife rotors, inner and outer knife rotors. The inner knife rotor carries a first cutting tool for cutting the cuttable pieces into slices and strips. The first cutting tool includes a plurality of plate-shaped knives and a plurality of sets of gate forming knives positioned in passage channels formed in the inner knife rotor. Each set of gate forming knives is positioned adjacent to and upstream of one of the plate-shaped knives. The gate forming knives first simultaneously cut the cuttable pieces into a plurality of strip sections. The associated plate-shaped knife then slices the strip sections to form individual strips, which are led out of the passage channel. The outer knife rotor carries a second tool, a plurality of plate-shaped knives, that cross cuts the strips coming out of the passage channels according to the desired length. Guides, which press the cuttable pieces against the first cutting tool, are arranged in the interior of the inner knife rotor. The guides can have either a spiral-shaped guideway fastened onto a housing door or rotating guiding vanes.