Abstract: To remove a solid tire from a wheel over which that tire has been pressed, a transverse groove is cut in the tread of the tire with a cutting apparatus so as to expose the underlying rim. Then the exposed portion of the rim is cut with a flame that is passed through the groove. Once the rim is severed, the tire is easily dislodged from the rim. The cutting apparatus includes a base on which the wheel is positioned and slideways extended away from the base generally parallel to the axis of rotation for the wheel on the base. A slide is located along the slideways. The slide carries a knife that is elongated in the direction of slide movement. The knife has a free end provided with a point and cutting edges diverging from the point. A threaded screw when turned down moves the slide and the knife thereon, and the path of the knife is such that its point enters the tire at one side of its tread and after passing axially through the tread emerges from the other side.