This invention related to a cutting system (100) for cutting carcass parts (112) while the carcass parts are carried by carriers (108) connected to and moved (111) by an overhang transport system (107). A detection device (101) is provided for determining a cutting position (105a) of an incoming carcass part. At least one cutting device (103) having an upwardly and downwardly facing surface structure is provided and a moving mechanism (104) mechanically connected to the at least one cutting device for controlling the position of the at least one cutting device on the basis of the determined cutting position, and a carcass displacement device arranged to initiate displacement of the carcass part away from the at least one cutting position while the carcass part or a resulting sub-part carried by a carrier is located between the upstream cutting edge and the downstream edge.