The microstructure, phase composition, and mechanical properties of dense and porous specimens made of biocompatible β-titanium alloy Ti-10Ta-2Nb-2Zr produced by selective laser melting (SLM) were investigated. An optimal processing window (volumetric energy density of 61.7–94.1 J/mm3) was established, yielding a relative density of up to 99.92%. The as-built condition exhibited a fine acicular α′-martensitic structure, which provided high strength (ultimate tensile strength of 642 MPa, yield strength of 552 MPa) together with a reduced elastic modulus of 88 GPa. Annealing at 900 °C resulted in recrystallization and formation of an equilibrium lamellar α+β structure, further decreasing the elastic modulus to 85 GPa while maintaining sufficient ductility (elongation ~20%). To mimic trabecular bone, triply periodic minimal surface (TPMS) structures (Schwartz, Gyroid, Split) with 50% porosity were fabricated. Their effective elastic modulus (9.1–9.6 GPa) is comparable to that of bone tissue, thus addressing the stress shielding issue. The obtained results demonstrate the high potential of the Ti-10Ta-2Nb-2Zr alloy and SLM technology for manufacturing personalized orthopedic implants with improved biomechanical compatibility.