We derive ages, metallicities, and abundance ratios ([α/Fe]) from the integrated spectra of 23 globular clusters in M31 by employing multivariate fits to two different stellar population models. We also perform a parallel analysis on 21 Galactic globular clusters as a consistency check and in order to facilitate a differential analysis. Our analysis shows that the M31 globular clusters separate into three distinct components in age and metallicity; we identify an old, metal-poor group (seven clusters), an old, metal-rich group (10 clusters), and an intermediate-age (3-6 Gyr), intermediate-metallicity ([Z/H]~-1) group (six clusters). This third group is not identified in the Galactic globular cluster sample. We also see evidence that the old, metal-rich Galactic globular clusters are 1-2 Gyr older than their counterparts in M31. The majority of globular clusters in both samples appear to be enhanced in α-elements, but the degree of enhancement is rather model-dependent. The intermediate-age globular clusters appear to be the most enhanced, with [α/Fe]~0.4. These clusters are clearly depressed in CN with respect to the models and the bulk of the M31 and Milky Way sample. Compared with the bulge of M31, M32, and NGC 205, these clusters most resemble the stellar populations in NGC 205 in terms of age, metallicity, and CN abundance. We infer horizontal branch morphologies for the M31 clusters using the Rose Ca II index and demonstrate that blue horizontal branches are not leading to erroneous age estimates in our analysis. We discuss and reject as unlikely the hypothesis that these objects are in fact foreground stars contaminating the optical catalogs. The intermediate-age clusters have generally higher velocities than the bulk of the M31 cluster population. Spatially, three of these clusters are projected onto the bulge region, and the remaining three are distributed at large radii. We discuss these objects within the context of the build-up of the M31 halo and suggest that these clusters possibly originated in a gas-rich dwarf galaxy, which may or may not be presently observable in M31.