A method for cutting a flexible glass ribbon includes directing the flexible glass ribbon to a flexible glass cutting apparatus including a laser. The flexible glass ribbon includes a first broad surface and a second broad surface that extend between a first edge and a second edge of the flexible glass ribbon. A laser beam is directed from the laser onto a region of the flexible glass ribbon. A crack is formed through the flexible glass ribbon using the laser beam. The crack is propagated along the flexible glass ribbon using the laser beam and a local mechanical deformation in the flexible glass ribbon.