An apparatus for the automated mechanical processing of pieces of meat conveyed in a row comprises a transporting device, a cutting device having a cutting head and a control device. The cutting device comprises a holding and guiding device on which the cutting head is movably arranged to execute separating cuts at an angle to the straight conveying direction along the straight movement path at a fixed guiding tilt angle (α). A transport belt forming a component of the transporting device and transporting the meat pieces in a lying manner passes continuously by the holding and guiding device. The cutting element which, for cutting, is formed by a rotationally driven circular blade limited at its height position over the transport belt. The control device correlates a velocity component (VT) of the movement velocity of the cutting head, which velocity component of the movement is in conveying direction with the conveying velocity of the meat pieces in the conveying direction when executing the separating cuts. The apparatus is used in particular to skin fish fillets, wherein a tail end section is cut off of the fish fillet with a chamfer cut that generates a fillet end chamfered at a slant as an insertion aid for drawing in the skin to be removed into the draw-in gap of a skinning machine.