PURPOSE: To cleanly polish the edge of a cutter in the water by housing grinding wheels in a water tank having a cutter inserting port.

CONSTITUTION: After rough polishing is finished, finish polishing is performed in succession. In this case, a lever 16 is leftward rotated, and a pin 17 is fitted and fastened to a fastenning tool 19. Thereby, a first grinding wheel 11 and a second grinding wheel 12 in a first water tank 2 separate from each other, and a fourth grinding wheel 14 elastically contacts with a third grinding wheel 13 in a second water tank 3. Then, a cutter A is inserted from a slit 8, and when an edge is applied to the third grinding wheel 13 and the fourth grinding wheel 14 and is pulled to this side, the finish polishing is performed. Also in this case, since the first grinding wheel 11 and the second grinding wheel 12 in the first water tank 2 separate from each other, even if these rotate at high speed, abrasion is not caused.