The interaction mechanisms between a dislocation and a twin boundary in nanotwinned face-centered cubic metals are well understood in terms of perfect coherent interfaces. Processes involving intrinsic incoherent twin boundary defects, however, remain largely unexplored, despite recent evidence suggesting that imperfect twin boundaries containing short kink-like step defects contribute notably to plastic deformation and twin stability in large nanotwinned grains. Here, molecular dynamics simulation is used to study the underlying interaction of screw dislocations with either 0° or 60° atomic-scale kink twin boundary defects, in order to understand how the presence of imperfect twin boundaries can alter hardening and ductility mechanisms in nanotwinned copper. It is found that kinked twin boundaries are effective in changing the mechanisms from direct dislocation transmission to dislocation absorption when the applied shear strain exceeds 1.06%, with pronounced hardening arising from such transformation. Hardening by dislocation pinning from individual kink steps is also manifest for 60° intersections. On the contrary, twin boundary defects produce no hardening at low applied strains when dislocation absorption at the twin boundary is already prevailing.