PURPOSE: To safely and reliably execute a work of grinding a core bit without using a hand, by a method wherein a case equipped with a grinding stone and a rotation mechanism is situated so as to allow delivery thereof in the moving region of the core bit of a cutting device.

CONSTITUTION: When the cutting edge of a core bit 3a is ground, a main frame 2 is first moved to separate the core bit 3a from a furnace wall 30. Parallel rings 8 and 8 are then lowered, and a case 7 is lowered from a position shown by a 2-dotted chain line to a position shown by a solid line. The core bit 3a is then lowered so that a cutting edge 3b and a grinding surface 5a of a grinding stone 5 are situated in a position where central axes are displaced from each other, and in addition to rotation of the core bit 3a, the grinding stone 5 is rotated to grind the cutting edge of the core bit 3a. During the work the grinding stone 5 is moved to the cutting edge side of the core bit 3a by a given distance, the grinding stone 5 is pressed with a force against the cutting edge to shave off a cutting edge 3b by a given amount for grinding. As noted above, a work of grinding the cutting edge 3b can be safely and reliably executed without using a hand.