The effect of an argon ion beam on the surface of sapphire is studied at different technological parameters: the ion energy, and the angle α between the sapphire surface and the ion-beam axis. The roughness of the sapphire surface is analyzed before and after ion polishing. The optimum ion-beam parameters are determined, at which the surface roughness after polishing decreases to 0.8 nm. At angles α = 20°–30°, the relief of the sapphire surface is found to become wavy. The study of the impact of the ion energy on the roughness of the sapphire surface in the 400–1200-eV range reveals that an increase in the energy of the ion beam to 1200 eV is accompanied with a decrease by 8.8 times in the roughness which falls below the level of 3 nm.