A solution-treated Cu-0.5Cr-0.05Zr-0.05Ti (wt.%) alloy was drawn into a large-depth cup implementing a two-stage deformation process in the present study, firstly using a ∅50 mm cylindrical punch and subsequently redrawn by a ∅34 mm punch. The redrawn cup wall was subjected to aging heat treatment up to 400 °C, 500 °C, and 600 °C for 2 h followed by water quenching to understand the microstructural evolution and its correlation with mechanical properties. These aging temperatures were adopted to simulate a similar environmental condition in which the inner liner of the thrust chamber of cryogenic and semi-cryogenic engines was exposed during satellite launching. It was identified that the above aging temperatures influenced the grain characteristics, recrystallization, and annealing twin formation significantly. The redrawn cup wall possessed semi-coherent bcc spherical Cr-rich precipitates with an average size of 1.8 ± 0.1 nm, which progressively increased to 5.5 ± 0.3 nm at 600 °C, while the precipitate volume fraction increased to a maximum of 1.2% at 500 °C. The precipitation mostly influenced the strength, while the recrystallization and twin formation governed the ductility during the aging. After an initial decrement at 400 °C, the yield strength of the aged specimen was increased to a maximum of 193 MPa with a concurrent increase in ductility to 24% upon the optimal aging at 500 °C. However, a higher increment in the strength than the ductility indicated the dominance of the precipitation. Further increase in the temperature to 600 °C reduced the strength while considerably enhancing the ductility. This was attributed to the highest recrystallization and twin fraction, as well as precipitate coarsening with reduced volume fraction. Moreover, precipitation strengthening prevailed in the aged specimens, unlike dislocation strengthening in the redrawn condition. The contribution from the former was maximum at 500 °C with a 52% share of the total estimated strength, whereas it was only 31% in the redrawn specimen.