Chemical mechanical polishing (CMP) of sapphire, GaN, and SiC substrates, which are categorized as hard-to-process materials, is demonstrated with a colloidal silica slurry under acidic and alkaline slurry pH conditions. Atomic level surface flatness was achieved by CMP and was confirmed to be equivalent to an almost ideally minimized surface roughness. By comparing the Preston coefficients under different slurry conditions, differences in the CMP properties among the three substrate materials and difficulties in the CMP of the GaN and SiC substrates are presented. The difference in CMP properties between the (0001) and (000-1) planes of GaN and SiC due to their non-revers crystallographical symmetry is also presented. Oxidation processes that occur during CMP of GaN and SiC are also discussed. By comparing the removal rate among GaN, SiC, and their oxides, it was found that the rate-limiting step in the total CMP process for GaN and SiC was surface oxidation reaction of GaN and SiC.