A driving force transmitting clutch device includes a main shaft; a first rotor rotatable around the main shaft; a second rotor rotatable around the main shaft; an inner sleeve member attached to the second rotor for engaging the first rotor, and being movable in an axial direction of the main shaft; an outer sleeve member for receiving the inner sleeve member therein; and a coil spring for urging the inner sleeve member in a direction that the inner sleeve member engages the first rotor and the outer sleeve. When a movement of the outer sleeve is stopped, the outer sleeve moves the inner sleeve for releasing the inner sleeve from the first rotor and for releasing the inner sleeve from the outer sleeve.