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The circuit quantum acoustodynamics which are studied in hybrid quantum system composed by artificial atoms and surface acoustic waves (SAWs) have drawn a lot of attention when exploring the nonclassical properties of phonons. In this paper, we propose a hybrid system for indirect coupling between multiple SAW resonators via auxiliary transmons. First, by eliminating the qubit degrees of freedom, the energy exchange between two SAW resonators can be observed. In the dispersive regime and suitable rotating frame, Fock state transition and entanglement can be realized between two SAW resonators. Second, by treating transmon as a qutrit and applying a classical driving for qutrit, the correlated phonon pairs between two SAW resonators will be detected. Moreover, by replacing the SAW resonators with acoustic-wave pumps, the acoustically induced transparency phenomenon is realized in our system. The transmon qutrit is potential to use as a switch for propagating acoustic waves, allowing the acoustic waves to be transmitted or backscattered.