Surface phase separation dynamics of an alloy grown by molecular beam epitaxy on a lattice mismatched layer is numerically studied by means of a phenomenological time-dependent Ginzburg-Landau type equation for the compositional order parameter held. The present model involves effects of the deposition rate and the coupling between the compositional field of the alloy and the stress field due to a misfit edge dislocation array at the buffer layer-substrate interface. From several computer simulation results, it is shown that the dislocation induced stress field might provide a novel way to stabilize and tune the final surface patterns of phase separating materials under some deposition conditions.