Due to the negative correlation between pressure resistance and waterborne sound insulation, low-impedance soundproof materials can hardly work in deep water. Here, we propose a new mechanism to circumvent this problem by employing a sandwich panel with designed dynamics quasi-zero-stiffness (QZS) truss cores. The latticed cores are made of programable curved beams, whose shape is carefully designed to meet the demand of both high-pressure resistance and dynamics QZS. An analytical model is developed to evaluate sound transmission of such panel. It is shown that the low-frequency sound insulation performance of the customized panel increases with the hydrostatic pressure and reaches its maximum when the QZS state is triggered. The effective pressure range of the proposed sandwich panel can be further programed by stacking QZS beam lattices of different static load plateaus. The proposed design strategy stems solely from the structural geometry of the curved beams and is therefore materials-insensitive. The linear/inverse relationships between static loading feature and characteristic mechanical properties/geometrical parameters, and the stacking arrangement of lattice bring out the programability of the panel’s bearing capacity. The design strategy, together with the established database, provides a feasible approach for underwater sound insulation of equipment subjected to elevated pressures.