Leaf photosynthesis, coral mineralization, and trabecular bone growth depend on triply periodic minimal surfaces (TPMSs) with hyperboloidal structure on every surface point with varying Gaussian curvatures. However, translation of this structure into tissue-engineered bone grafts is challenging. This article reports the design and fabrication of high-resolution three-dimensional TPMS scaffolds embodying biomimicking hyperboloidal topography with different Gaussian curvatures, composed of body inherent β-tricalcium phosphate, by stereolithography-based three-dimensional printing and sintering. The TPMS bone scaffolds show high porosity and interconnectivity. Notably, compared with conventional scaffolds, they can reduce stress concentration, leading to increased mechanical strength. They are also found to support the attachment, proliferation, osteogenic differentiation, and angiogenic paracrine function of human mesenchymal stem cells (hMSCs). Through transcriptomic analysis, we theorize that the hyperboloid structure induces cytoskeleton reorganization of hMSCs, expressing elongated morphology on the convex direction and strengthening the cytoskeletal contraction. The clinical therapeutic efficacy of the TPMS scaffolds assessed by rabbit femur defect and mouse subcutaneous implantation models demonstrate that the TPMS scaffolds augment new bone formation and neovascularization. In comparison with conventional scaffolds, our TPMS scaffolds successfully guide the cell fate toward osteogenesis through cell-level directional curvatures and demonstrate drastic yet quantifiable improvements in bone regeneration.