A corrugated board web cutting device comprising: one slitter device which forms cutting lines (SL1_o,SL2_o,SL1_n,SL2_n) in a corrugated board web along a transfer direction to create a plurality of slitted webs (25U,25D); a plurality of cutoff devices (17U,17D) which cut the plurality of slitted webs (25U,25D) along a width direction; a director device which is disposed between the slitter device and the plurality of cutoff devices (17U,17D) to separate along separation cutting lines (DL_n,DL_o) cut by the slitter device the plurality of slitted webs (25U,25D) cut by the slitter device and distribute the slitted webs (25U,25D) to the plurality of cutoff devices (17U,17D); a separation cutting device which is disposed further on the upstream side than the director device; is movable in the width direction of the corrugated cardboard web; and cuts, when the slitter device is temporarily stopped cutting the corrugated cardboard web due to a change in the order of the slitted web (25U,25D), the corrugated cardboard web to form a separation cutting line connecting the separation cutting line (DL_n) of a new order and the separation cutting line (DL_o) of an old order; and a control device which controls an operation of the separation cutting device, characterized in that: when the separation cutting device forms the separation cutting line, the separation cutting device cuts the corrugated cardboard web while moving in the width direction from the position of the separating cutting line (DL_o) of the old order to the position of the separating cutting line (DL_n) of the new order to form a cutting line oblique to the transport direction, and when it reaches the position of the separation cutting line of the new order, stops the movement in the width direction and the separation cutting device continues a cutting operation for a predetermined time or by a predetermined cutting length after the movement in the width direction is stopped at a position of the separation cutting line (DL_n) of the new order to form a cutting line along the transfer direction. one slitter device which forms cutting lines (SL1_o,SL2_o,SL1_n,SL2_n) in a corrugated board web along a transfer direction to create a plurality of slitted webs (25U,25D); a plurality of cutoff devices (17U,17D) which cut the plurality of slitted webs (25U,25D) along a width direction; a director device which is disposed between the slitter device and the plurality of cutoff devices (17U,17D) to separate along separation cutting lines (DL_n,DL_o) cut by the slitter device the plurality of slitted webs (25U,25D) cut by the slitter device and distribute the slitted webs (25U,25D) to the plurality of cutoff devices (17U,17D); a separation cutting device which is disposed further on the upstream side than the director device; is movable in the width direction of the corrugated cardboard web; and cuts, when the slitter device is temporarily stopped cutting the corrugated cardboard web due to a change in the order of the slitted web (25U,25D), the corrugated cardboard web to form a separation cutting line connecting the separation cutting line (DL_n) of a new order and the separation cutting line (DL_o) of an old order; and a control device which controls an operation of the separation cutting device, characterized in that: when the separation cutting device forms the separation cutting line, the separation cutting device cuts the corrugated cardboard web while moving in the width direction from the position of the separating cutting line (DL_o) of the old order to the position of the separating cutting line (DL_n) of the new order to form a cutting line oblique to the transport direction, and when it reaches the position of the separation cutting line of the new order, stops the movement in the width direction and the separation cutting device continues a cutting operation for a predetermined time or by a predetermined cutting length after the movement in the width direction is stopped at a position of the separation cutting line (DL_n) of the new order to form a cutting line along the transfer direction.