The relation between galaxy stellar mass and gas-phase metallicity is a sensitive diagnostic of the main processes that drive galaxy evolution, namely inflow of relatively pristine gas from the intergalactic medium, metal production in stars, and metal ejection via galactic winds. Previous mass- metallicity relations based on strong line metallicity measurements suffer from large systematic uncertainties that impact the physical interpretation of the mass-metallicity relation. We stacked the spectra of ~200,000 star-forming galaxies from the SDSS to significantly enhance the signal-to-noise ratio of the weak [O III] 4363 and [O II] 7320, 7330 auroral lines required to measure metallicity with the more relibable direct method. The direct method mass- metallicity relation spans a wide range in stellar mass and extends an order of magnitude lower in stellar mass than strong line mass-metallicity relations. We investigated how deviations from the mean direct method mass- metallicity relation correlate with SFR and found a factor of two to three times stronger correlation with SFR than strong line mass-metallicity relations, which implies that galaxies require a longer timescale to re-enrich themselves following the accretion of pristine gas. The steep low mass slope and comparatively low normalization of the direct method mass-metallicity relation indicate that galactic winds efficiently eject metals from galaxies, particularly low mass galaxies.