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.　©　2020,　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature.