Nanotwinned materials have attracted widespread attention due to their superior mechanical properties, such as high strength, good ductility and work hardening. Experimental and molecular dynamics (MD) simulation results had indicated that there are three distinctly different dislocation-mediated deformation mechanisms in nanotwinned metals, namely dislocation pile-up against and slip transfer across twin boundaries (TBs), Shockley partials gliding on twin boundaries leading to twin boundary migration, and threading dislocations slip confined by neighboring twin boundaries. However, most of the previous studies are focused on the homogenous plastic deformation under tension and compression tests, the non-homogenous deformation and its deformation mechanism, especially under low strain and complex stress condition/confined condition, of nanotwinned metals are still not explored so far. In this study, the electrodeposited bulk Cu samples with preferentially oriented nanotwins were cold rolled with the normal of the rolling plane parallel to the growth direction (ND//GD) to strain of 15% at room temperature. The microstructure features of as-rolled Cu were investigated by SEM and TEM. Microstructure evolution indicates that many detwinning bands appeared in the direction about 30°~45° with respect to the rolling direction, which is the direction with the largest shearing stress. The twin lamellae in the detwinning bands coarsened obviously. Based on calculation of the local shear strain and strain gradient of TBs in a selected detwinning band, it indicates that the maximum shear strain occurs in the middle of the deformation bands, and its detwinning mechanism is directly related the localized shear strains (γ). The twin lamellae in the detwinning bands were coarsened obviously. When 0.3<γ<0.8, the detwinning process via producing amount of Shockley dislocations on twin boundaries dominates the deformation. After detwinning, Shockley partial dislocations stored at the area with the maximum strain gradient and formed incoherent twin boundaries (ITBs). The present investigation indicates detwinning process dominates the plastic deformation and sustains the local shearing strain in nanotwinned Cu at small strains under cold rolling.