Triply Periodic Minimal Surface (TPMS) structures, particularly the Gyroid topology, are promising candidates for lightweight energy absorber design owing to their homogeneous stress distribution, curved interconnections, and high specific energy absorption. In this study, a Gyroid structure with dimensions of 80×80×80 mm was fabricated from PLA+ via Fused Deposition Modeling (FDM) and subjected to quasi-static compression testing using a 15-ton Santam universal testing machine. A finite element model developed in Abaqus was validated against experimental force–displacement responses and subsequently employed for systematic parametric investigation. The effects of wall thickness (1–4 mm) and Y-direction scale factor (1.2–3.0) on specific energy absorption (SEA) were evaluated, and optimization was performed using Response Surface Methodology based on a Central Composite Design (CCD) in Design Expert software. Results demonstrated that SEA peaks at a wall thickness of 3 mm and declines beyond this value due to a transition in failure mechanisms, while a Y-direction scale factor of 2.0 consistently yielded the highest SEA across all wall thickness groups. Single-objective RSM optimization refined the optimal design point to a scale factor of 2.522 and wall thickness of 3.382 mm, yielding a predicted SEA of 7,921.78 J/kg—a value that confirms and precisely locates the performance peak identified through parametric analysis. These findings establish wall thickness and directional scale factor as effective and accessible geometric parameters for maximizing the mass-normalized energy absorption capacity of Gyroid TPMS structures fabricated via additive manufacturing.