Zn-based alloys are recognized as promising bioabsorbable materials for cardiovascular stents, due to their biocompatibility and favorable degradability as compared to Mg. However, both low strength and intrinsic mechanical instability arising from a strong strain rate sensitivity and strain softening behavior make development of Zn alloys challenging for stent applications. In this study, we developed binary Zn-4.0Ag and ternary Zn-4.0Ag-xMn (where x= 0.2-0.6wt%) alloys. An experimental methodology was designed by cold working followed by a thermal treatment on extruded alloys, through which the effects of the grain size and precipitates could be thoroughly investigated. Microstructural observations revealed a significant grain refinement during wire drawing, leading to an ultrafine-grained (UFG) structure with a size of 700 nm and 200 nm for the Zn-4.0Ag and Zn-4.0Ag-0.6Mn, respectively. Mn showed a powerful grain refining effect, as it promoted the dynamic recrystallization. Furthermore, cold working resulted in dynamic precipitation of AgZn3 particles, distributing throughout the Zn matrix. Such precipitates triggered mechanical degradation through an activation of Zn/AgZn3 boundary sliding, reducing the tensile strength by 74% and 57% for Zn-4.0Ag and Zn-4.0Ag-0.6Mn, respectively. The observed precipitation softening caused a strong strain rate sensitivity in cold drawn alloys. Short-time annealing significantly mitigated the mechanical instability by reducing the AgZn3 fraction. The ternary alloy wire showed superior microstructural stability relative to its Mn-free counterpart due to the pinning effect of Mn-rich particles on the grain boundaries. Eventually, a shift of the corrosion regime from localized to more uniform was observed after the heat treatment, mainly due to the dissolution of AgZn3 precipitates.