To easily carry out temporary fastening and complete fastening of a cutter whose a plurality of edges are laminated with each other in same positions while relatively facing to a grinding wheel and while arranging a swaging surface upward, in a swaging surface grinding device for a cutter, which is used after mounting and fixing it on a chuck upper surface of a longitudinal cutter grinding disk.

An inclining block 2, a crest receiving block 3, and a bearing 11 received a supporting shaft 12 for slidably supporting a cramp arm 13, are integratedly fixed to an upper surface of a base 5 which is removably mounted and fixed to the upper surface of a chuck 5. An installing hole position of the cramp arm 13 is slid from a centroid of the cramp arm 13 to a tip end side, and a hydraulic cylinder 14 is vertically arranged so as to push up the rear end part lower surface of the cramp arm 13.