A computer-controlled band saw sharpener employing electrically powered, X and Y axis drivers, each having a reciprocating element. The X-axis driver actuates a feed finger mechanism, to index the saw in repetitive, stepped fashion, while each tooth is successively ground. In concert with the X-axis driver, the Y axis driver repetitively lowers and raises a grinding head, provided with a rotary grinding wheel. Both the X and Y axis drivers include servomotors to rotate the shaft of an elongated ball screw. A carrier box houses a non-rotatable ball screw nut. The nut travels back and forth along the ball screw shaft in accordance with its direction and extent of rotation. Drive arms for the feed finger mechanism and the grinding head mechanism are bolted at their lower ends to a threaded bushing in the nut carrier box. The computerized controller is programmable, to produce virtually any desired tooth shape in the saw. Standard-tooth profiles, variable-pitch tooth profiles, and variable depth tooth profiles may be selected by touching a button on the controllers panel.