A medical cutting device for producing thin cartilage disks has a device body with a first holding device with a first working section having a first recess disposed on a top side of the device body such that the first recess is entirely or partially enclosed by a first delimiting ridge and, a connecting section that is directly, rigidly adjoined by the first working section and a cover with a counterpart section to the connecting section that is directly, rigidly adjoined by a first pressure section, which comprises a central, first pressure plate that is resiliently held in the first pressure section and, in an operating state for producing thin cartilage disks, is disposed opposite the first recess, which is entirely or partially enclosed by the first delimiting ridge.