In this study, hydroxyapatite (HAp)-reinforced polylactic acid (PLA) matrix composite filaments were successfully fabricated. HAp powders were synthesized via the thermal calcination method and subsequently incorporated into the PLA matrix using a twin-screw extruder. To ensure homogeneous distribution, each formulation was extruded at least three times. Three-dimensional vertebral models were then produced using the HAp-reinforced PLA filaments, and their physical as well as mechanical properties were systematically evaluated. The results revealed that, compared to pure PLA, the composite-based models exhibited a reduction of 66.7% in tensile strength and 22.5% in compressive strength. To improve mechanical behaviour, thermoplastic elastomer (TPE) was added, which enhanced the performance of the composite models. Furthermore, to mimic the trabecular bone structure, triply periodic minimal surface (TPMS) infill geometries, triply periodic minimal surface (TPMS) geometries were employed as infill patterns. Four TPMS designs—Gyroid, Schwarz Primitive, Schwarz Diamond, and 3D Hex—were investigated at infill ratios of 15%, 20%, and 25%. Compression and pull-out tests were performed on the TPMS-based vertebral models. Among the tested configurations, the 25% Gyroid infill demonstrated the most favourable performance, achieving average values of 32 kN in compression and 9.96 kN in pull-out strength. These findings suggest that HAp- and TPE-modified PLA filaments with TPMS structures are promising materials for the fabrication of bio-inspired vertebral models with enhanced mechanical properties.