The behavior of sputtering yield and the surface roughness of monocrystalline silicon of orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩ under the ion-beam bombardment by neutralized Ar ions with energies of 200-1000 eV is studied. The significant dependence (modulation) of sputtering yield on incidence angle due to crystalline structure is observed. It is shown that a sharp increase in the sputtering yield and a decrease in the effective surface roughness at energies above 400 eV occurs. At energies of more than 400 eV for orientations ⟨100⟩, ⟨110⟩, and ⟨111⟩ at normal ion incidence, smoothing of the effective roughness in the range of spatial frequencies ν∈[4.9⋅10-2-6.3⋅101µm-1] up to a value of 0.17 nm is observed. This makes it possible to use the ion-beam etching technique for finishing polishing, aspherization, and correction of local shape errors of single-crystal silicon substrates, which are of the greatest interest for synchrotrons of the 3rd+ and 4th generation and x-ray free electron lasers.