Architectured materials are increasingly considered for lightweight structural applications due to their tunable mechanical properties. However, despite recent advances in additive manufacturing, no standardized methodology exists for their mechanical characterization, as classical testing standards (such as ISO 6892-1 for tensile testing and ASTM E9 for compression testing) are not directly applicable to lattice-based structures produced by powder bed fusion processes. This work addresses the experimental–numerical characterization of metallic architectured materials based on a triply periodic minimal surface (TPMS) geometry, namely the gyroid lattice. Two specimen designs are proposed to enable tensile and compressive experimental testing under well-controlled and representative loading conditions. The specimens are manufactured using the Laser Powder Bed Fusion (LPBF) process. A finite element–based model is proposed with a twofold objective: to support the design of specimens and experiments. Static simulation are used to ensure that stress localization and failure occur within the lattice region rather than in the gripping zones. Quasi-static tensile and compressive experiments are then conducted, and global force–displacement responses are compared with numerical predictions. To gain further insight into the local mechanical behavior, full-field displacement measurements are obtained using digital image correlation (DIC). The experimental displacement fields are used to analyze strain localization and deformation mechanisms within the gyroid architecture and to provide quantitative data for the validation of the numerical models. The final objective of this study is to establish a correlation between experiments and finite element simulations to identify an equivalent homogeneous mechanical behavior for the selected lattice architectures. The predictive capability of FE modeling for TPMS based architectured materials is assessed, with the aim of contributing to reliable design, sizing, and characterization methodologies for additively manufactured architectured structures.