In recent years, Zn-based materials have been extensively investigated as potential candidates for biodegradable implant applications. The introduction of alloying elements providing solid-solution strengthening and second phase strengthening seems crucial to provide a suitable platform for the thermo-mechanical strengthening of Zn alloys. In this study, a systematic investigation of the microstructure, crystallographic texture, phase composition, and mechanical properties of a Zn–3Ag-0.5Mg (wt%) alloy processed through combined hot extrusion (HE) and cold rolling (CR), followed by short-time heat treatment (CR + HT) at 200 °C was conducted. Besides, the influence of different annealing temperatures on the microstructure and mechanical properties was studied. An adequate combination of processing conditions during CR and HT successfully addressed brittleness obtained in the high-strength HE Zn–3Ag-0.5Mg alloy. By controlling the microstructure, the most promising results were obtained in the sample subjected to 50% CR reduction and 5-min annealing, which were: ultimate tensile strength of 432 MPa, yield strength of 385 MPa, total elongation to failure of 34%, and Vickers microhardness of 125 HV0.3. The obtained properties clearly exceed the mechanical benchmarks for biodegradable implant materials. Based on the conducted investigation, brittle multi-phase Zn alloys' mechanical performance can be substantially enhanced to provide sufficient plasticity by grain refinement through cold deformation process, followed by short-time annealing to restore proper strength.