We present the metallicities and carbon abundances of four newly discovered metal-poor stars with $ -2.2 <$ [Fe/H] $< -1.6$ in the Sagittarius dwarf spheroidal galaxy. These stars were selected as metal-poor member candidates using a combination of public photometry from the SkyMapper Southern Sky Survey and proper motion data from the second data release from the Gaia mission. The SkyMapper filters include a metallicity-sensitive narrow-band $v$ filter centered on the Ca II K line, which we use to identify metal-poor candidates. In tandem, we use proper motion data to remove metal-poor stars that are not velocity members of the Sagittarius dwarf spheroidal galaxy. We find that these two datasets allow for efficient identification of metal-poor members of the Sagittarius dwarf galaxy to follow-up with further spectroscopic study. Two of the stars we present have [Fe/H] $< -2.0$, which adds to the few other such stars currently identified in the Sagittarius dwarf galaxy that are likely not associated with the globular cluster M54, which resides in the nucleus of the system. Our results confirm that there exists a very metal-poor stellar population in the Sagittarius dwarf galaxy. We find that none of our stars can be classified as carbon-enhanced metal-poor stars. Efficiently identifying members of this population will be helpful to further our understanding of the early chemical evolution of the system.