We　propose　a　scheme　to　achieve　nuclear-nuclear　indirect　interactions　mediated　by　a　mechanically　driven　nitrogen-vacancy　(NV)　center　in　a　diamond.　Here　we　demonstrate　two-qubit　entangling　gates　and　quantum-state　transfer　between　two　carbon　nuclei.　When　the　dipole-dipole　interaction　strength　is　much　larger　than　the　driving　field　strength,　the　scheme　is　robust　against　decoherence　caused　by　coupling　between　the　NV　center　(nuclear　spins)　and　the　environment.　Conveniently,　precise　control　of　dipole　coupling　is　not　required　so　this　scheme　is　insensitive　to　fluctuating　positions　of　the　nuclear　spins　and　the　NV　center.　Our　scheme　provides　a　general　blueprint　for　multi-nuclear-spin　gates　and　for　multi-party　communication.