We present a catalog of Fe, Mg, Si, Ca, and Ti abundances for 2961 stars in eight dwarf satellite galaxies of the Milky Way (MW): Sculptor, Fornax, Leo I, Sextans, Leo II, Canes Venatici I, Ursa Minor, and Draco. For the purposes of validating our measurements, we also observed 445 red giants in MW globular clusters and 21 field red giants in the MW halo. The measurements are based on Keck/DEIMOS medium-resolution spectroscopy (MRS) combined with spectral synthesis. We estimate uncertainties in [Fe/H] by quantifying the dispersion of [Fe/H] measurements in a sample of stars in monometallic globular clusters (GCs). We estimate uncertainties in Mg, Si, Ca, and Ti abundances by comparing to high-resolution spectroscopic abundances of the same stars. For this purpose, a sample of 132 stars with published high-resolution spectroscopy in GCs, the MW halo field, and dwarf galaxies has been observed with MRS. The standard deviations of the differences in [Fe/H] and <[{alpha}/Fe]> (the average of [Mg/Fe], [Si/Fe], [Ca/Fe], and [Ti/Fe]) between the two samples is 0.15 and 0.16, respectively.