A stitch flap cutting block is mountable to a cutting head of a board blank cutting machine, along with a slotting knife. A sheet of board passed between the cutting head and an anvil head is cut to form a blank for a box or the like. The cutting block comprises a steel body with a cylindrical barrel holding a cylindrical spring block, to which is mounted a blade holder carrying an elongate blade. The blade moves within a transverse slot across the body and is deflectable into the body and may rock about a midpoint of the slot. Impact forces are reduced, cleaner cuts are produced, and re-setting of the blade is required much less often. An alternative stitch flap cutting block is mountable to the cutting head by a separate side arm, facilitating mounting to cutting heads having different diameters.