Abstract: An apparatus for cutting sheet glass which can not only cut a glass sheet into several smaller sheets of different sizes by a single operation but also can form cutting lines on several glass sheets by superposing them one over the other in sequence without dismounting the preceding sheets from the cutting apparatus after forming cutting lines thereon so as to obtain several smaller sheets of different sizes from each large glass sheet, and also a cutter which inhibits the formation of jagged irregularities on the cut faces of the smaller sheets when separated along the cutting lines.