A molecular dynamics study was performed on the mechanical response of thermal-pressure rejuvenated CuxZr100−x metallic glasses. The effect of temperature (50, 300, 600 K) and pressure (0–50 GPa) on the rejuvenation process and the mechanical properties of CuxZr100−x including stress–strain response, shear localization formation and elastic modulus were investigated. The thermal-pressure rejuvenation process involves transitioning the system to a higher potential energy state and a lower atomic volume, demonstrating the significant influence of pressure on rejuvenation. Our findings reveal that increasing pressure at specific temperatures and material compositions results in reduced yield stress and stress drop. They also indicate that with increasing pressure, the system undergoes a transition towards homogeneity, resulting in enhanced ductility compared to its initial amorphous state. Additionally, high temperatures contribute to lower values of Young's, shear, and bulk moduli, as well as decreased yield stress and stress drop. Consequently, the system becomes more homogeneous, promoting rejuvenation. Furthermore, we observed that the final yield strength of the system increases with higher Cu content for all structures at specific pressures and temperatures. The level of rejuvenation is additionally impacted by the amount of Cu, and structures containing varying content of Cu demonstrate varying degrees of rejuvenation. To validate our findings, we utilized Voronoi analysis, which revealed a higher fraction of densely-packed clusters in the samples. Finally, a total of 10 materials properties were calculated and explored using statistical analysis which shows there are different correlations between pressure, temperature and atomic composition with mechanical properties.