There are provided surgical suturing apparatus or stitching devices particularly suited for use in suturing artificial heart valves to heart tissue during heart valve replacement surgery. The disclosed apparatus include a stationary jaw oriented at a predetermined angle relative to the apparatus to facilitate suturing through the artificial valve in a direction generally parallel to the axis of the valve. One embodiment of the stitching device utilizes a pair of surgical needles or incision members joined by a single length of suture material. There are also disclosed disposable loading units for providing suture - needle assemblies to the suturing apparatus. Also disclosed are methods of suturing an artificial heart valve to heart tissue using the disclosed apparatus.