An apparatus for cutting sheet materials comprises a support frame for supporting the material to be worked and a cutting tool operatively movably connected to the support frame and effective to move from a retracted position to a cutting position. Means are provided to drive the cutting tool without interruption in one continuous cutting cycle from a fully retracted position to a cutting position, then to an intermediate position between the cutting and retracted positions, then back to a cutting position substantially immediately, and thereafter to the fully retracted position. This is accomplished by a driving mechanism comprising conventional toggle arms driven by a piston which moves from a withdrawn position to a fully extended position and back to the withdrawn position during the cutting cycle. The toggle arms are driven past their position of alignment twice during the movement of the piston and this is effective to reciprocally drive the cutting tool twice into cutting position during a single cycle. As a result, the material is quickly cut at the same location twice in succession, thereby ensuring a complete and accurate severing action.