Inspired by Scylla serrata, a novel thermoplastic polyurethane (TPU) negative Poisson's ratio sign-switching metamaterial is proposed, and the corresponding original and gradient structures (i.e., OPSM and GPSM) are created. Numerical simulation is utilized to simulate the quasi-static and dynamic compression behavior of the proposed structures considering the rate-dependent properties, elastoplastic response, and nonlinear contact. The neo-Hookean hyperelastic constitutive model and the Prony series are adopted to model the target structures. Finite element results are validated through experimental results. Parametric studies are conducted to study the effects of gradient characteristics and loading velocities on the mechanical behavior and Poisson's ratio of the structures. Testing results indicate that the proposed novel bioinspired structure patterns exhibit fascinating mechanical behavior and interesting negative Poisson's ratio sign-switching characteristics, which would provide the design guidance for the development and application of bioinspired structural materials.