Abstract: A machine particularly useful for sawing diamonds and other precious stones comprises a pair of horizontally-spaced posts on a stationary frame, each post having a socket open at its upper end of rotatably supporting the horizontal trunnions of a vertical sawing disc holder, each open socket being closable by a cap carried on the inner face of a cover pivotably mounted to each of the posts. The described machine further includes a swingable arm pivotably mounted at one end to the stationary frame, a workpiece holder carried by the opposite end of the swingable arm and rotatable about its longitudinal axis, a threaded pin fixed to the workpiece holder and rotatable therewith about the longitudinal axis of the swingable arm, and a stop fixed to the swingable arm and engageable by the threaded pin to locate the workpiece holder at a predetermined angular position with respect to the swingable arm and to the vertical sawing disc holder.