A sheet material cutting apparatus in which a pair of blades comprising a movable blade and a fixed blade are arranged, and the movable blade reciprocates to cut sheets. A drive device is mounted on the cutting apparatus, which drive device includes a drive arm to actuate the movable blade and a connecting lever having a split groove for connecting the lever to the drive arm. The movable blade is driven with the aid of the connecting lever and the drive arm of the drive device. The drive of the movable blade is controlled by elasticity of the split groove in the connecting lever. When load exceeding a predetermined amount occurs at the movable blade, the split groove in the connecting lever permits the drive arm to come off.