In this work, we show that remote heteroepitaxy can be achieved when Cu thin film is grown on single crystal, monolayer graphene buffered sapphire(0001) substrate via a thermal evaporation process. X-ray diffraction and electron backscatter diffraction data show that the epitaxy process forms a prevailing Cu crystal domain, which is remotely registered in-plane to the sapphire crystal lattice below the monolayer graphene, with the (111) out-of-plane orientation. As a poor metal with zero density of states at its Fermi level, monolayer graphene cannot totally screen out the stronger charge transfer/metallic interactions between Cu and substrate atoms. The primary Cu domain thus has good crystal quality as manifested by a narrow crystal misorientation distribution. On the other hand, we show that graphene interface imperfections, such as bilayers/multilayers, wrinkles and interface contaminations, can effectively weaken the atomic interactions between Cu and sapphire. This results in a second Cu domain, which directly grows on and follows the graphene hexagonal lattice symmetry and orientation. Because of the weak van der Waals interaction between Cu and graphene, this domain has inferior crystal quality. The results are further confirmed using graphene buffered spinel(111) substrate, which indicates that this remote epitaxial behavior is not unique to the Cu/sapphire system.