Abstract: A system for cutting windows or openings in mats used in framing works of art. The system involves the use of a variably positionable head to which a cutting blade is attached for cutting a beveled edge in the mat. A longitudinal drive means, transverse drive means, and orthogonal drive form a combined positioning device capable of moving the head in any direction. A rotational drive means may also form part of the combined positioning device for rotating and adjusting the position of the blade. A linear variable displacement transducer is coupled to the head and operatively coupled to the orthogonal drive to maintain the head a constant distance away from the mat so the blade cuts a continuously smooth beveled edge in the mat.