In recent years, twinned nanopillars have attracted tremendous attention for research due to their superior mechanical properties. However, most of the studies were focused on nanopillars with twin boundaries (TBs) perpendicular to loading direction. Nanopillars with TBs parallel to loading direction have received minimal interest. In this backdrop, the present study is aimed at understanding the role of axial TBs on strength and deformation behaviour of Cu nanopillars using atomistic simulations. Tensile and compression tests have been performed on <112> nanopillars with and without TBs. Twinned nanopillars with twin boundary spacing in the range 1.6-5 nm were considered. The results indicate that, under both tension and compression, yield strength increases with decreasing twin boundary spacing and is always higher than that of perfect nanopillars. Under compression, the deformation in <112> perfect as well as twinned nanopillars proceeds by the slip of extended dislocations. In twinned nanopillars, an extensive cross-slip by way of Friedel-Escaig and Fleischer mechanisms has been observed in compression. On the other hand, under tensile loading, the deformation in perfect nanopillars occurs by partial slip/twinning, while in twinned nanopillars, it proceeds by the slip of extended dislocations. This extended dislocation activity is facilitated by stair-rod formation and its dissociation on the twin boundary. Similar to compressive loading, the extended dislocations under tensile loading also exhibit cross-slip activity in twinned nanopillars. However, this cross-slip activity occurs only through Fleischer mechanism and no Friedel-Escaig mechanism of cross-slip has been observed under tensile loading.