A rotary shearing apparatus for slitting sheet material into a plurality of strips of predetermined width is disclosed. The apparatus comprises a plurality of tool carriages each having upper and lower tool-holding members supporting upper and lower shearing tools, respectively, and mounted for axial movement in a machine frame for ease of positioning of the tool carriages and replacement of the shearing tools when necessary. Mechanisms are provided for adjusting the vertical overlap of the shearing tools and for automatically moving the tool carriages independently of one another at high or low speed to vary the spacing between the tool carriages and thereby adjust the width of the strips to be slit from the sheet material.