A polishing method and a polishing apparatus capable of polishing a surface of a substrate made of SiC or diamond extremely smoothly and efficiently without causing subsurface damage are provided. A polishing platen 1 can rotate around a rotating shaft 4, and is made of quartz having high transparency to ultraviolet radiation. A large number of grooves 11 are arranged on a front surface of the polishing platen 1 in a lattice form, and each of the grooves 11 is filled with solid photocatalytic particles 20 (CeO2). The polishing platen 1 is relatively rubbed against a to-be-polished surface 30A of a substrate 30 made of silicon carbide (SiC) or diamond (C) while pressing the polishing platen 1 to the to-be-polished surface 30A of the substrate 30 with a very high pressure, thereby the to-be-polished surface 30A is oxidized by the solid photocatalytic particles 20 to perform chemical polishing. The oxidation of the to-be-polished surface 30A is promoted by applying ultraviolet radiation from an ultraviolet source lamp 2, and polishing is promoted by heating by an infrared source lamp 3.