A series of biodegradable Mg-Cu alloys is designed to induce osteogenesis, stimulate angiogenesis, and provide long-lasting antibacterial performance at the same time. The Mg-Cu alloys with precipitated Mg2Cu intermetallic phases exhibit accelerated degradation in the physiological environment due to galvanic corrosion and the alkaline environment combined with Cu release endows the Mg-Cu alloys with prolonged antibacterial effects. In addition to no cytotoxicity towards HUVECs and MC3T3-E1 cells, the Mg-Cu alloys, particularly Mg-0.03Cu, enhance the cell viability, alkaline phosphatase activity, matrix mineralization, collagen secretion, osteogenesis-related gene and protein expressions of MC3T3-E1 cells, cell proliferation, migration, endothelial tubule forming, angiogenesis-related gene, and protein expressions of HUVECs compared to pure Mg. The favorable osteogenesis and angiogenesis are believed to arise from the release of bioactive Mg and Cu ions into the biological environment and the biodegradable Mg-Cu alloys with osteogenesis, angiogenesis, and long-term antibacterial ability are very promising in orthopedic applications.