Cu with nanotwin (NT) possesses great electrical, mechanical, and thermal properties and has potential for electronic applications. Various studies have reported the effect of NT orientation on Cu mechanical properties. However, its effect on Cu stress-relaxation behavior has not been clarified, particularly in nano-scale. In this study, Cu nanopillars with various orientations were examined by a picoindenter under constant strain and observed by in situ TEM. The angles between the twin plane and the loading direction in the examined nanopillars were 0°, 60°, to 90°, and a benchmark pillar of single-crystal Cu without NT was examined. The stress drops were respectively 10%, 80%, 4%, and 50%. Owing to the interaction by NT, the dislocation behavior in nanopillars was different from that in bulk or in thin film samples. Especially, the rapid slip path of dislocations to go to the free surface of the nanopillar induced a dislocation-free zone in the 0° nanopillar, which led to work-softening. On the contrary, a high dislocation density was observed in the 90° nanopillar, which was generated by dislocation interaction and obstruction of dislocation slip by twin planes, and it led to work-hardening. The findings reveal the NT orientation in Cu nanopillars affected stress relaxation significantly.