The invention discloses a blasting cutting device with a composite charging structure and a construction method of the blasting cutting device. The blasting cutting device is composed of a shaped blasting tube, a tail connector, explosives, a detonating cord and a reverse detonating cartridge, wherein the shaped blasting tube comprises an explosive groove with a horn-shaped groove and an outer buckling explosive groove cover; a tube is filled with the explosives and is provided with the detonating cord; the reverse detonating cartridge can be connected with the tail of the tube through the tail connector, and therefore the blasting cutting device is formed; and the blasting cutting device is fixed in a blasting hole by a positioning block. According to the horn-shaped groove in the shapedexplosive tube, the charging structure of the horn-shaped groove can generate higher jet velocity than the charging structure of a cone-angle-shaped groove, and the cutting ability on rock mass is higher. The shaped blasting tube has two types including a common type and a reinforced type. A groove of the common type shaped blasting tube is an opening, a groove notch of the reinforced type shapedblasting tube is closed, a shaped cavity is formed in the groove, on the one hand, the rigidity of the structure can be enhanced, on the other hand, after water is injected into the shaped cavity, high-pressure jet water can be generated during blasting to form a water jet, the cutting ability on the rock mass can be enhanced, and the generated water mist can further play a role in dust removal.