Studies of the early chemical evolution of some larger dwarf galaxies ( $>10^7$ solar masses) are limited by the small number of stars known at low metallicities in these systems. Here we present metallicities and carbon abundances for eighteen stars with metallicities between $-3.08 le text{[Fe/H]} le -1.47$ in the Sagittarius dwarf spheroidal galaxy, using medium-resolution spectra from the MagE spectrograph on the Magellan-Baade Telescope. This sample more than doubles the number of known very metal-poor stars ([Fe/H] $leq -2.0$) in the Sagittarius dwarf galaxy, and identifies one of the first known extremely metal-poor stars ([Fe/H] $leq -3.0$) in the system. These stars were identified as likely metal-poor members of Sagittarius using public, metallicity-sensitive photometry from SkyMapper DR1.1 and proper motion data from Gaia DR2, demonstrating that this dearth of metal-poor stars in some dwarf galaxies can be addressed with targeted searches using public data. We find that none of the stars in our sample are enhanced in carbon, in contrast to the relative prevalence of such stars in the Milky Way halo. Subsequent high-resolution spectroscopy of these stars would be key in detailing the early chemical evolution of the system.