Functional microvasculature is essential for in vitro tissue constructs, ensuring efficient transport of oxygen, nutrients, and waste and supporting vital paracrine signaling for tissue stability. Recent advancements in both direct and indirect 3D bioprinting offer promising solutions to construct complex vascular networks by allowing precise control over cell and extracellular matrix placement. The process from shape printing of microvasculature to function formation involves dynamic shift of bioink mechanical properties, mechanical microenvironments, and mechanobiology of endothelial and supporting cells. This review explores how biomechanical and mechanobiological principles are integrated into the bioprinting process to develop functional microvascular networks. Before printing, a top-level design approach based on these principles focuses on the interactions among biomaterials, cell behaviors, and mechanical environments to guide microvascular network fabrication. During printing, biomechanical design of bioinks for different bioprinting techniques, along with optimized biomechanical factors of bioprinting process, ensures accurate microvascular structure reproduction while maintaining cell viability. After printing, the emphasis is on creating a suitable mechanical environment to modulate the mechanobiology of multiple steps of neovascularization, including initiation, morphogenesis, lumen formation, stabilization, and maturation of functional microvasculature. Finally, we discuss future developments based on biomechanical and mechanobiological design to drive the bioprinting of functionalized microvascular networks.