The Cu–Cr–Ni alloy is a key material for the manufacturing of connectors, which requires excellent resistance to stress relaxation. However, the inherent correlation among microstructure, texture, and properties is still unclear. In this study, we investigated the influence of calefaction and stress relaxation on the grain boundaries (GBs), textures, and properties of the Cu–Cr–Ni alloy. The results showed that calefaction and stress relaxation had opposite effects on GBs and textures. Calefaction led to a decrease in the proportion of low-angle grain boundaries (LAGBs), an increase in the Schmidt factor (SF) value of the grains, and a transition of texture from <111> to <113>. The grains with higher SF values were more susceptible to plastic deformation, which deteriorated the stress relaxation resistance. By comparison, stress relaxation led to an increase in the proportion of LAGBs, a decrease in SF values of the grains, and a transition of texture from <113> to <111> and <001>. After stress relaxation, the variation trends of the GBs and textures were consistent with those of other plastic deformations, indicating that stress relaxation can be verified by the variations in GBs and textures. Our findings provide a theoretical basis for improvements in stress relaxation resistance of the Cu-based alloys used in connector industry.