Molecular dynamics simulations have been performed to understand the variations in deformation mechanisms of Cu nanowires as a function of orientation and loading mode (tension or compression). Cu nanowires of different crystallographic orientations distributed uniformly on the standard stereographic triangle have been considered under tensile and compressive loading. The simulation results indicate that under compressive loading, the orientations close to $<$100$>$ corner deform by twinning mechanism, while the remaining orientations deform by dislocation slip. On the other hand, all the nanowires deform by twinning mechanism under tensile loading. Further, the orientations close to $<$110$>$ and $<$111$>$ corner exhibit tension-compression asymmetry in deformation mechanisms. In addition to deformation mechanisms, Cu nanowires also display tension-compression asymmetry in yield stress. The orientations close to $<$001$>$ corner exhibits higher yield stress in tension than in compression, while the opposite behaviour (higher yield stress in compression than in tension) has been observed in orientations close to $<$110$>$ and $<$111$>$ corners. For the specific orientation of $<$102$>$, the yield stress asymmetry has not been observed. The tension-compression asymmetry in deformation mechanisms has been explained based on the parameter $alpha_M$, defined as the ratio of Schmid factors for leading and trailing partial dislocations. Similarly, the asymmetry in yield stress values has been attributed to the different Schmid factor values for leading partial dislocations under tensile and compressive loading.