Soft polymer materials are often used in shock absorption, cushioning, and so on. During the design and development process, determining the mechanical behavior and constitutive properties under static and dynamic loads is important to improve product performance. This study aims to analyze the static mechanical performance of polyvinyl chloride elastomers with different Shore hardness levels. Static and dynamic mechanical performance experiments with loading strain rates of 0.1, 1650, 2000, and 2700 s−1 were performed in polyvinyl chloride elastomers (57A, 52A, and 47A) using an electronic dynamic and static fatigue tester and an improved Split Hopkinson pressure bar. Microstructures were observed by scanning electron microscopy. Results showed that the addition of plasticizers to polyvinyl chloride promoted the crystallization of the polymer. The presence of plasticizer in the crystal also reduced crystallization. The material plasticity, elastic modulus, yield stress, and flow stress increase with increasing hardness/strain rate, whereas the hardness decreases. The mechanical behavior of polyvinyl chloride elastomers under static and dynamic loads exhibited superelastic and viscoelastic characteristics, respectively. The Mooney–Rivlin, Neo–Hookean, and Yeoh models were selected for the superelastic constitutive model, whereas the Zhu–Wang–Tang model was used for the viscoelastic one. Finally, the applicability of the model was explained. This study can provide theoretical model and method support for the design and development of soft polymer materials.