Zn is a promising biodegradable metal owing to its moderate degradation rate and acceptable biocompatibility. However, the insufficient mechanical strength and plasticity of pure Zn limits its application in bone implants. In this study, a spiral eutectic structure is constructed in Zn–Mg–Ag alloys prepared via selective laser melting to improve their mechanical properties. Results show that the prepared Zn–Mg–Ag alloys are composed of a primary Zn matrix and a eutectic phase, which is composed of alternating α-Zn and an intermetallic compound, MgZn2. Moreover, the eutectic phase resembles a spiral and increases with Ag content in the alloys. The eutectic pinning effect hinders dislocation and hence results in dislocation accumulation. Meanwhile, the spiral structure alters the propagation direction and dissipates the propagation energy of cracks layer by layer. Consequently, a compressive strength of up to 309 ± 15 MPa and an improved strain of 27% are exhibited in Zn–3Mg–1Ag alloy. Moreover, the Zn–Mg–Ag alloys show high biocompatibility with MG-63 cells and antibacterial activity against Escherichia coli. These findings indicate the potential of spiral eutectic structures for enhancing both the mechanical strength and plasticity of biodegradable Zn alloys.