A hard crystal substrate such as a GaN substrate or a SiC substrate is polished by using polishing oil slurry having abrading particles of artificial diamond clusters dispersed in a dispersant. The artificial diamond clusters include approximately spherical agglomerate particles with average particle size D50 of 20 nm or more and 50 nm or less, having primary particles with particle diameters of 2 nm or more and 10 nm or less. A rough polishing process is carried out first such that an average surface roughness of 0.5 nm or more and 1 nm or less is obtained, followed by a finishing process such that the average surface roughness of said surface becomes 0.2 nm or less.