In this work, an integrated multiscale simulation of magnetron sputtering epitaxy was conducted to study the effect of sputtering pressure on the surface micro-topography of sputtered Cu/Si films. Simulation results indicated that, as the sputtering pressure increased from 0.15 to 2 Pa, the peak energy of the incident energy distribution gradually decreased from 2 to 0.2 eV, which might be mainly due to the gradual decrease in the proportion of deposited Cu atoms whose energy ranged from 2 to 30 eV; the peak angle of the incident polar angle distribution increased from 25° to 35°, which might be attributed to the gradual thermalization of deposited Cu atoms; the growth mode of Cu film transformed from the two-dimensional layered mode to the Volmer-Weber mode. The transformation mechanism of growth mode was analyzed in detail. A comprehensive analysis of the simulation results indicated that incident energy ranging from 2 to 30 eV and incident angle between 10° and 35° might be conducive to the two-dimensional layered growth of sputtered Cu films. This work proposes an application-oriented modeling approach for magnetron sputtering epitaxy.