Abstract: To obtain a quality-meat-attached backbone part suitable as a material for minced fish the invention proposes cutting off a fin part and a kidney from a meat-attached backbone part obtained when filleting a fish into three pieces. The meat-attached backbone part is conveyed by a pair of upper and lower conveyor belts while being sandwiched and held between the belts. When the backbone part reaches a fin cutter arranged in a midstream of the conveyance, a belly part is pushed by a first pushing lever while a back part of the meat-attached backbone part is received and stopped by a receiving and stopping lever, and the back skin from a back fin to a tail fin is cut off by the fin cutter. Then, when the meat-attached backbone part reaches a kidney cutter, the belly part of the meat-attached backbone part is pushed by a second pushing lever to position the kidney-attached backbone section of the meat-attached backbone part at a cutting position by a kidney cutter.