The invention relates to a special-shaped surface polishing device and method.The special-shaped surface polishing device comprises a polishing medium, a six-axis mechanical arm, polishing liquid jetting equipment, polishing liquid sprinkling equipment and a workpiece clamping and rotating platform, the polishing medium comprises an imbedding layer and a polishing layer which are arranged in a stacked mode, and a first groove is formed in the upper surface of the imbedding layer; a second groove is formed in the face, making contact with the imbedding layer, of the polishing layer, a pressure sensor and a temperature sensor are arranged in the imbedding layer, and a polishing structure of the polishing layer is matched with a to-be-polished face; and the polishing medium is made of microporous polyurethane. The polishing medium made of the microporous polyurethane material is selected, foaming holes of the microporous polyurethane facilitate the fluidity of polishing powder, the polishing medium comprises the imbedding layer and the polishing layer which are arranged in a stacked mode, grooves are formed in each layer, the fluidity of polishing liquid is improved, the polishing efficiency is improved, the polishing medium is grabbed through the six-axis mechanical arm, and the polishing medium is convenient to replace.