A joint compound sanding machine imparting an oscillating motion on an abrasive within a sanding plane and on a removable abrasive extension comprises a hand held housing and an oscillating base. The base is coupled to the hand held housing by a motor. The base comprises a bottom surface defining the sanding plane, a clamp for securing the abrasive against the bottom surface, and a mounting for securing the removable abrasive extension to the base. The motor is coupled between the hand held housing and the base for imparting the oscillating motion, with respect to the hand held housing, on the base to oscillate both the abrasive and the removable abrasive extension.