Large galaxies grow through the accumulation of dwarf galaxies. In principle it is possible to trace this growth history using the properties of a galaxys stellar halo. Previous investigations of the galaxy M31 (Andromeda) have shown that outside a radius of 25 kpc the population of halo globular clusters is rotating in alignment with the stellar disk, as are more centrally located clusters. The M31 halo also contains coherent stellar substructures, along with a smoothly distributed stellar component. Many of the globular clusters outside 25 kpc are associated with the most prominent substructures, while others are part of the smooth halo. Here we report a new analysis of the kinematics of these globular clusters. We find that the two distinct populations are rotating with perpendicular orientations. The rotation axis for the population associated with the smooth halo is aligned with the rotation axis for the plane of dwarf galaxies that encircles M31. We interpret these separate cluster populations as arising from two major accretion epochs, likely separated by billions of years. Stellar substructures from the first epoch are gone, but those from the more recent second epoch still remain.