Additive manufacturing has been used to develop a variety of scaffold designs for clinical and industrial applications. Mechanical properties (i.e., compression, tension, bending, and torsion response) of these scaffolds are significantly important for load-bearing orthopaedic implants. In this study, we designed and additively manufactured porous metallic biomaterials based on two different types of triply periodic minimal surface structures (i.e., gyroid and diamond) that mimic the mechanical properties of bone, such as porosity, stiffness, and strength. Physical and mechanical properties, including compressive, tensile, bending, and torsional stiffness and strength of the developed scaffolds, were then characterised experimentally and numerically using finite element method. Sheet thickness was constant at 300 μm, and the unit cell size was varied to generate different pore sizes and porosities. Gyroid scaffolds had a pore size in the range of 600–1200 μm and a porosity in the range of 54–72%, respectively. Corresponding values for the diamond were 900–1500 μm and 56–70%. Both structure types were validated experimentally, and a wide range of mechanical properties (including stiffness and yield strength) were predicted using the finite element method. The stiffness and strength of both structures are comparable to that of cortical bone, hence reducing the risks of scaffold failure. The results demonstrate that the developed scaffolds mimic the physical and mechanical properties of cortical bone and can be suitable for bone replacement and orthopaedic implants. However, an optimal design should be chosen based on specific performance requirements.