We present a new method to engineer the charge carrier mobility and its directional asymmetry in epitaxial graphene by using metal cluster superlattices self-assembled onto the moiré pattern formed by graphene on Ir(111). Angle-resolved photoemission spectroscopy reveals threefold symmetry in the band structure associated with strong renormalization of the electron group velocity close to the Dirac point giving rise to highly anisotropic Dirac cones. We further find that the cluster superlattice also affects the spectral-weight distribution of the carbon bands as well as the electronic gaps between graphene states.