In this work, we study the phase-space and chemical properties of the Sagittarius (Sgr) stream, the tidal tails produced by the ongoing destruction of the Sgr dwarf spheroidal (dSph) galaxy, focusing on its very metal-poor (VMP; [Fe/H] < −2) content. We combine spectroscopic and astrometric information from SEGUE and Gaia EDR3, respectively, with data products from a new large-scale run of the StarHorse spectrophotometric code. Our selection criteria yield ∼1600 stream members, including >200 VMP stars. We find the leading arm (b > 0°) of the Sgr stream to be more metal-poor, by ∼0.2 dex, than the trailing one (b < 0°). With a subsample of turnoff and subgiant stars, we estimate this substructure’s stellar population to be ∼1 Gyr older than the thick disk’s. With the aid of an N-body model of the Sgr system, we verify that simulated particles stripped earlier (>2 Gyr ago) have present-day phase-space properties similar to lower metallicity stream stars. Conversely, those stripped more recently (<2 Gyr) are preferentially akin to metal-rich ([Fe/H] > −1) members of the stream. Such correlation between kinematics and chemistry can be explained by the existence of a dynamically hotter, less centrally concentrated, and more metal-poor population in Sgr dSph prior to its disruption, implying that this galaxy was able to develop a metallicity gradient before its accretion. Finally, we identified several carbon-enhanced metal-poor ([C/Fe] > +0.7 and [Fe/H] ≤ −1.5) stars in the Sgr stream, which might be in tension with current observations of its remaining core where such objects are not found.