In the field of high-speed vehicles, it is crucial to understand the aeroelastic response of a panel backed with a cavity subjected to an impinging oblique shock, which involves nonlinear aerodynamic loads, large deformable structures, and the mutual interaction between the structure and acoustic field. Most researchers have assumed a constant acoustic pressure within the cavity and ignored the dynamic coupling properties between the acoustic field and the structure when investigating the cavity effect on the flutter behavior of the panel. In this paper, to fill this gap, an implicitly partitioned numerical method is proposed for fluid-structure-acoustic strong coupling iterative calculations of three physical fields, such as high-speed compressible fluid, large-deformable plate, and sound wave in acoustic cavity. The method is formulated with the unsteady Navier-Stokes equations in an arbitrary Lagrangian-Eulerian finite volume framework, the geometrical nonlinear composite laminated beam model which based on the general higher-order shear deformation zig-zag theory and discretized by the finite element method, and the linear acoustic wave equation for the stationary compressible inviscid acoustic fluid in the cavity. The impacts of acoustic fluid density, cavity pressure, and cavity depth on the aerodynamic response of the panel-cavity system subjected to an oblique shock are studied. Some new findings are revealed. The alterations in the physical parameters of the cavity prompt a transition in the vibration regime of the panel-cavity aeroelastic system, shifting from a fixed-point stable regime to an asymmetric periodic limit cycle oscillation regime. The study reveals a strong mutual interaction between the acoustic cavity and the panel, where the acoustic pressure load opposes the motion of the panel, a phenomenon attributed to the 'spring effect' of the enclosed fluid. Notably, for certain depth ratios, the acoustic modal properties of the cavity altered the distribution of acoustic pressure loads applied to the panel, thereby reducing the critical flutter dynamic pressure.