Commercially pure Cu was processed through high-pressure torsion (HPT) up to a shear strain of 1000 and naturally aged for 1.75 years by keeping the samples under laboratory conditions. Hardness of the freshly processed samples monotonically increased with the HPT strain; however, the samples processed to a shear strain of 2 to 20 demonstrated a remarkable drop in the hardness values after the natural ageing. Interestingly, the natural ageing was not effective in changing the hardness of HPT processed samples strained up to very high shear strains. Electrical resistivity of the HPT processed samples after natural ageing showed a non-monotonous variation with the HPT strain, wherein it increased and then decreased and finally again started to increase with increasing shear strain. A discussion on the role of total length of boundaries, which was measured using electron back-scattered diffraction technique, and residual stresses, which was measured using X-ray diffraction, in determining hardness and resistivity is presented to qualitatively understand the origin of the non-monotonous variations of these two properties in the commercially pure Cu. It is suggested that besides residual stress, crystal defects, such as dislocations and vacancies, might also play important roles in determining the effect of HPT processing on resistivity of Cu.