Additive manufacturing enables the fabrication of lightweight structures with complex geometries, offering significant potential in aerospace and biomedical applications. Triply periodic minimal surface (TPMS) lattice structures are of particular interest due to their geometry. However, their intricate geometries pose challenges for both experimental characterization and numerical simulation. This study numerically investigates the effective mechanical properties and dynamic response of AlSi10Mg TPMS structures produced by laser powder bed fusion (PBF-LB/M). Using a micro–mesoscale approach with periodic boundary conditions, Young’s modulus, shear modulus, and Poisson’s ratio in the elastic region using the Johnson–Cook plasticity model are analyzed. Finite element simulations of the representative volume element (RVE) are employed to assess energy absorption and damage evolution under high strain rates, incorporating a ductile damage model. The performance of sheet-based TPMS lattices, namely, Schwarz–Primitive, Gyroid, Schwarz–Diamond, and IWP, is compared with strut-based lattices, namely, BCC and FCC, across volume fractions of 20–40%. Results demonstrate the superior stiffness and energy absorption of TPMS lattices, where Schwarz–Diamond and IWP outperformed the other structures, highlighting their advantages over conventional strut-based designs. This comprehensive numerical framework provides new insights into the high strain-rate behavior of TPMS structures and supports their design for demanding engineering applications.