The response of small-grained metals to mechanical stress is investigated by a theoretical study of the elementary mechanisms occurring during the shear-coupled migration of grain boundaries (GB). Investigating a model 17(410) GB in a copper bicrystal, both 110 and 100 GB migration modes are studied focusing on both the structural and energetic characteristics. The minimum energy paths of these shear-coupled GB migrations are computed using the nudge elastic band method. For both modes, the GB migration occurs through the nucleation and motion of disconnections. However, the atomic mechanisms of both modes qualitatively differ: While the 110 mode presents no metastable state, the 100 mode shows multiple metastable states, some of them evidencing some kinks along the disconnection lines. Disconnection kinks nucleation and motion activation energies are evaluated. Besides, the activation energies of the 100 mode are smaller than those of the 110 one except for very high stresses. These results significantly improve our knowledge of the GB migration mechanisms and the conditions under which they occur.