A method of cutting a strengthened glass plate includes irradiating a laser beam 20 on a front surface 12 of a strengthened glass plate 10 and moving an irradiation area 22 of the laser beam 20 on the front surface 12 of the strengthened glass plate 10 to cut the strengthened glass plate 10 by causing a crack that penetrates the strengthened glass plate 10 in the thickness direction at the back of the irradiation area 22. By irradiating the laser beam 20 to the front surface 12 of the strengthened glass plate 10, the intermediate layer 17 at the irradiation area 22 is heated to a temperature less than or equal to an annealing point and the propagation of the crack is suppressed by generating a tensile stress less than the internal remaining tensile stress in the intermediate layer 17 or the compression stress at the center of the irradiation area 22.