Using molecular dynamics simulations, we systematically investigate shock-induced migration of a set of Σ3〈110〉70.53° tilt grain boundaries in Cu, including coherent twin boundary, 15 asymmetric tilt grain boundaries (ATGBs), and symmetric incoherent twin boundary (SITB), with inclination angle (Φ) increasing from 0° to 90°. Grain boundary migration occurs only in ATGBs, via faceting for Φ≤70.53° and translation for Φ>70.53° (with the 9R phase). Migration magnitude increases with increasing Φ for ATGBs. Migration mode and magnitude depend on the grain boundary structure including SITB orientation and length fraction, and the symmetry of resolved shear stress distribution across a grain boundary.