Ion beam machining technology has been extensively adopted to obtain an ultraprecision surface in ultraviolet lithography optics. However, there exist complex mechanisms leading the surface to evolve complicated topographies and increasing roughness. We build a kinetic model integrating with the typical sputter theory and a bond-counting Monte Carlo algorithm based on the compound materials to investigate the surface roughness evolution during ion beam sputtering. The influences of primary sputter, reflection, secondary sputter, geometrical shadowing, redeposition, and thermal diffusion were all taken into consideration to compose a dynamic evolution process. In calculation, using this model the surface first possesses a period of smoothing and then goes into a roughening stage, where the roughness follows the regular power law. Quantitative analyses of surface roughness derived from calculations are also examined and compared with experiments.