We report molecular dynamics simulations and their analysis for a mixed tilt and twist grain boundary vicinal to the Σ7 symmetric tilt boundary of the type {123} in aluminum. When minimized in energy at 0K, a grain boundary of this type exhibits nanofacets that contain kinks. We observe that at higher temperatures of migration simulations, given extended annealing times, it is energetically favorable for these nanofacets to coalesce into a large terrace-facet structure. Therefore, we initiate the simulations from such a structure and study as a function of applied driving force and temperature how the boundary migrates. We find the migration of a faceted boundary can be described in terms of the flow of steps. The migration is dominated at lower driving force by the collective motion of the steps incorporated in the facet, and at higher driving forces by the step detachment from the terrace-facet junction and propagation of steps across the terraces. The velocity of steps on terraces is faster than their velocity when incorporated in the facet, and very much faster than the velocity of the facet profile itself, which is almost stationary. A simple kinetic Monte Carlo model matches the broad kinematic features revealed by the molecular dynamics. Since the mechanisms seem likely to be very general on kinked grain-boundary planes, the step-flow description is a promising approach to more quantitative modeling of general grain boundaries.