This study investigated the effects of four heat treatment processes on the microstructure, damping capacity, and mechanical properties of Mn-Cu alloys. The results indicated that the alloy did not undergo spinodal decomposition and twinning after solution treatment. After solution and aging treatment, the alloy underwent spinodal decomposition and formed Mn-rich regions, increasing the martensitic transformation temperature (M_s), promoting martensitic transformation, forming twin boundaries, and enhancing damping capacity and mechanical properties. The cryogenic treatment and furnace cooling process facilitated the process, promoted the formation of twin boundaries, and improved damping capacity, and the degree of promotion by furnace cooling process was more significant. In addition, cryogenic treatment promoted grain refinement, increased dislocation density, improved strength, and facilitated the improvement of mechanical properties. This provided a reference for preparing high-damping Mn-Cu alloys with good comprehensive performance.