The invention relates to a GXJ steel rubber water stop band connector box lateral stripping device and a construction method thereof. The GXJ steel rubber water stop band connector box lateral stripping device comprises a connector box body, at least one pair of jacks arranged in the connector box body, and an oil channel structure. The connector box body comprises a base plate and a cover plate which are connected, an end face with a continuous turning curve is formed on the cover plate, an installation groove where a GXJ steel rubber water stop band is placed is formed in the front end of the cover plate, the jacks are symmetrically arranged on the two sides of the installation groove of the connector box body, and the oil channel structure is connected between the jacks and a hydraulic station to control the jacks to be jacked out of the cover plate. According to the GXJ steel rubber water stop band connector box lateral stripping device and the construction method thereof, the jacks are arranged in the connector box body and connected to the hydraulic station, power is provided, a piston of an oil cylinder pushes a piston cap, the connector box body is jacked away from the concrete end face of a front construction groove section, the connector box body is hoisted through hoisting equipment, lateral stripping is carried out, a complete water stop band is ensured, and the influence on the concrete quality is small.