A method of cutting a stack structure and the stack structure are disclosed. In the stack structure comprising at least one laser absorbing member and at least one laser transmitting member, a plurality of grooves are formed on the surface of the laser transmitting member which is in contact with the laser absorbing member, which grooves correspond to a plurality off cutting lines. In order to cut this stack structure, a laser beam is emitted on the laser absorbing member along each of the cutting lines, while at the same time gas is injected at the laser irradiated spot.