Three-dimensional (3D) bioprinting has emerged as a transformative biofabrication technology capable of engineering complex tissue constructs for regenerative medicine. While considerable progress has been made in replicating soft tissues using hydrogel-based bioprinting, the fabrication of mechanically robust bone-mimicking constructs remains a significant challenge. The mechanical heterogeneity of bone, including its anisotropic structure, varying mineral density, and intricate extracellular matrix (ECM) composition, complicates the development of bioinks that simultaneously ensure printability, structural integrity, and cellular viability. Recent advancements have focused on optimizing the mechanical properties of bioinks through composite hydrogels, osteoinductive nanomaterials, and bioactive moieties that enhance cell adhesion and differentiation. This review examines the role of mechanical cues in directing mesenchymal stem cell (MSC) fate, the interplay between material stiffness and osteogenesis, and strategies to enhance bioink performance. We highlight limitations in mechanical compliance and propose novel biomaterial designs, crosslinking strategies, and scaffold functionalization to overcome these barriers. This review aims to bridge the gap between biomaterials science and clinical translation, advancing functional bone graft substitutes.