A wire-cut electric discharge machine having a function of cutting a wire electrode, comprising: an upper wire guide and a lower wire guide that respectively guide the wire electrode on upper and lower sides of a workpiece; first wire electrode cutting energizing electrodes (20; 20a, 20b) that are provided on the upper side of the upper wire guide on a travelling path of the wire electrode, and hold the wire electrode; second wire electrode cutting energizing electrodes that are provided on a lower stream side compared to the first wire electrode cutting energizing electrodes (20; 20a, 20b); a tensile force imparting part configured to impart predetermined tensile force to the wire electrode; a cooling part configured to cool down a part, on which the first wire electrode cutting energizing electrodes (20; 20a, 20b) and the wire electrode contact with each other; wherein the first wire electrode cutting energizing electrodes (20; 20a, 20b) and the second wire electrode cutting energizing electrodes are arranged to energize the wire electrode for heating of the wire electrode, and the tensile force imparting part is arranged to impart the wire electrode with the tensile force, at the same time, so that the wire electrode is cut, characterised in that the wire-cut electric discharge machine further comprises a driving part which is configured to move the first and second wire electrode cutting energizing electrodes (20; 20a, 20b, 22) relative to the wire electrode so as to clamp the wire electrode at a desired position wherein the driving part is a first air cylinder valve for performing a closing operation of the first and second wire electrode cutting energizing electrodes (20; 20a, 20b; 22) with the wire electrode; and an air solenoid valve for supplying air to the first air cylinder valve and to a second air cylinder valve of the cooling part for supplying the cooling medium, whereby the second air cylinder valve is opened and closed in conjunction with the first air cylinder valve. an upper wire guide and a lower wire guide that respectively guide the wire electrode on upper and lower sides of a workpiece; first wire electrode cutting energizing electrodes (20; 20a, 20b) that are provided on the upper side of the upper wire guide on a travelling path of the wire electrode, and hold the wire electrode; second wire electrode cutting energizing electrodes that are provided on a lower stream side compared to the first wire electrode cutting energizing electrodes (20; 20a, 20b); a tensile force imparting part configured to impart predetermined tensile force to the wire electrode; a cooling part configured to cool down a part, on which the first wire electrode cutting energizing electrodes (20; 20a, 20b) and the wire electrode contact with each other; wherein the first wire electrode cutting energizing electrodes (20; 20a, 20b) and the second wire electrode cutting energizing electrodes are arranged to energize the wire electrode for heating of the wire electrode, and the tensile force imparting part is arranged to impart the wire electrode with the tensile force, at the same time, so that the wire electrode is cut, characterised in that the wire-cut electric discharge machine further comprises a driving part which is configured to move the first and second wire electrode cutting energizing electrodes (20; 20a, 20b, 22) relative to the wire electrode so as to clamp the wire electrode at a desired position wherein the driving part is a first air cylinder valve for performing a closing operation of the first and second wire electrode cutting energizing electrodes (20; 20a, 20b; 22) with the wire electrode; and an air solenoid valve for supplying air to the first air cylinder valve and to a second air cylinder valve of the cooling part for supplying the cooling medium, whereby the second air cylinder valve is opened and closed in conjunction with the first air cylinder valve.