The excitation spectrum of graphene on Cu (111), probed by momentum-resolved electron-energy-loss spectroscopy, exhibits multiple acoustic surface plasmons (ASP), arising from both the graphene overlayer and the Cu (111) substrate. We have investigated the mutual interaction between the ASP of the graphene overlayer and that of the underlying Cu (111) substrate. The weak interaction between graphene and Cu (111) implies that the ASP of Cu (111) survives, with only slight changes in its group velocity. Remarkably, we find that the damping processes of ASP are mitigated as compared to the cases of other graphene/metal interfaces. Therefore, this interface is an ideal graphene/metal contact for graphene-based plasmonics. Moreover, the presence of graphene coating protects the ASP of Cu (111) from quenching in an ambient atmosphere.