The apparatus (1) includes a horizontally supported transport drum (11), spaced-apart endless belts (51) that revolve around rollers (54.1 to 54.8) and are partially wrapped around the transport drum (11) such that an infeed (14) and an outlet (15) are formed and the cardboard cuttings (2, 3) are pressed against and conveyed on the drum. Groove cutting tools (72) are arranged between the belts (51). In order to allow a visual inspection of the cut grooves (3a) from above during the operation of the apparatus, the outlet (15) is situated in the region of the upper vertex of the transport drum (11). The delivery of the grooved cardboard cuttings (3) at the upper vertex of the transport drum (11) also results in an ergonomically advantageous removal height.