The Triply Periodic Minimal Surface (TPMS) structures, as a new type of lattice porous superstructure, possess high designability and the absence of stress concentration. However, there has been limited research on their vibration characteristics. Therefore, it is of great significance to conduct comprehensive research on the static mechanical characteristics and vibration isolation mechanical characteristics of TPMS structures. Firstly, this research established a geometric model of P-type unit cells based on implicit surfaces, and prepared TPMS isolator specimens using Thermoplastic Polyurethane (TPU). Secondly, the influence of structural parameters on static mechanical properties was studied through the finite element model. The parameter identification of the constitutive model of TPMS isolator substrate was completed through tensile experiments, and the constitutive relationship of TPU was studied. A quasi-static compression finite element model of TPMS isolator was constructed, and the accuracy of the finite element model was verified by combining the quasi-static compression experimental results. The equivalent elastic modulus of TPMS isolators was calculated based on finite element models for different porosities. The Ashby Gibson model between porosity and equivalent elastic modulus was successfully established. Finally, based on vibration transmission rate experiments, the influence of different loads on the isolation performance of TPMS isolators was studied, and the dynamic stiffness and equivalent damping of the structure were analyzed. A dynamic model of porosity for TPMS isolators was established to describe and predict their dynamic behavior, and the effectiveness of the established dynamic model was verified through experimental results.