In the recent decades, zinc (Zn) and its alloys have been drawing attention as promising candidates for bioresorbable cardiovascular stents due to its degradation rate more suitable than magnesium (Mg) and iron (Fe) alloys. However, its mechanical properties need to be improved in order to meet the criteria for vascular stents. This work investigates the mechanical properties, biodegradability and biocompatibility of Zn-Mg and Zn-Cu alloys in order to determine a proper alloy composition for optimal stent performance. Nanoindentation measurements are performed to characterize the mechanical properties at the nanoscale as a function of the Zn microstructure variations induced by alloying. The biodegradation mechanisms are discussed and correlated to microstructure, mechanical performance and bacterial/cell response. Addition of Mg or Cu alloying elements refined the microstructure of Zn and enhanced yield strength (YS) and ultimate tensile strength (UTS) proportional to the volume fraction of secondary phases. Zn-1Mg showed the higher YS and UTS and better performance in terms of degradation stability in Hanks’ solution. Zn-Cu alloys presented an antibacterial effect for S. aureus controlled by diffusion mechanisms and by contact. Biocompatibility was dependent on the degradation rate and the nature of the corrosion products.