An annular cutter connecting apparatus includes an arbor, annular cutter fixing locking members received in holding holes formed in the lower end portion of the arbor and a sleeve member surrounding the lower end portion of the arbor, for fixing an annular cutter to the arbor. The sleeve has a first control face having an inner diameter equal to the outer diameter of the lower end portion of the arbor, for projecting the locking members into the central bore by a predetermined length when the first control face engages the locking members, and second control faces formed circumferentially in the first control face, for receiving the locking members. The sleeve is rotatable around its own axis so as to cause the locking members to selectively face the first control face and the second control faces, respectively. An annular cutter has a shank portion provided with locking member passing portion or portions on that part of the outer peripheral surface of the shank portion which corresponds to the holding holes of the annular cutter connecting apparatus. The shank portion has depressed locking member receiving portion formed in or on the locking member passing portion or portions and receive the locking members. The annular cutter is connected to and removed from the arbor in one-touch operation.