Friction stir processing (FSP), a severe plastic deformation process, was applied on pure Cu to obtain a stir zone with a very fine grain size. Yet, when FSP is used, the stir zone is as wide as the diameter of the shoulder at the upper surface of the weld and markedly narrower near its opposite surface. This property, as well as the differences between the advancing side and the retreating side, makes it impossible to obtain a uniform cross-section as far as the microstructure and mechanical properties are concerned. For these reasons, a new approach is proposed in which the material was processed on both sides, thus yielding a wider, rectangular and more homogenous stir zone from which all the specimens were machined out. Processing the material from both sides eliminated any microstructural difference between the upper and the lower side, at least within the gauge length’s cross-section of the creep specimens. Although grain refinement was detected, the mechanical properties of the friction-stir-processed (FSP’ed) material are inferior relative to those of the parent material. The TEM study reported in the current paper revealed the existence of nanosized grains in the FSP’ed material due to dynamic recrystallization (DRX) occurring during the processing stage. Because both X-ray inspection and fractography showed that the FSP’ed material was free of defects, the material may not comply with the Hall–Petch relation due to lower dislocation density caused by XRD occurring during FSP. The inverse Hall–Petch effect may also be considered as an assistive mechanism in mechanical property deterioration.