Ground-state cooling is a crucial issue in cavity magnomechanical systems, which have emerged as a prominent platform for quantum detection technology due to their operational flexibility. In this paper, we propose a scheme to cool the magnomechanical resonator to its ground state in a double-cavity magnomechanical system, where mutually coupled cavities are simultaneously coupled to the resonator. In this scheme, we find the magnomechanical resonator can be cooled to its ground state via the magnomechanical interaction, and the cooling effect in a dual cavity is higher than that in a single cavity. In particular, ground-state cooling can be achieved even with a somewhat weak coupling strength by adjusting the coupling between two cavities and the coupling between the magnon and phonon to attain better cooling conditions. These results offer a valuable path to achieve the cooling of the magnomechanical mode.