To explore the chemo-structural properties of galaxies and understand quantitatively the cycling of baryons at the peak epoch of cosmic star formation, I developed a highly effective method for sub-kiloparsec scale spatially resolved spectroscopy of strongly lensed galaxies using space-based wide-field slitless grism data. Applying this method to the deep Hubble Space Telescope (HST) near-infrared grism observations, I obtained precise gas-phase metallicity maps for a large sample of star-forming galaxies in the redshift range of 1.2 ≲ z ≲ 2.3. Over half of the galaxies in my sample reside in the dwarf mass regime (Mstar ≲ 10^9 Msun), making my sample the first statistically representative sample of high-redshift dwarf galaxies with their metallicity spatial distribution measured with sufficient resolution. The metallicity maps obtained in my work reveal a variety of baryonic physics, such as efficient radial mixing from tidal torques, rapid accretion of low-metallicity gas, and various feedback processes which can significantly influence the chemo-structural properties of star-forming galaxies. For the first time, I discovered two dwarf galaxies at z~2 displaying strongly inverted metallicity radial gradients, suggesting that powerful galactic winds triggered by central starbursts carry the bulk of stellar nucleosynthesis yields to the outskirts. I also observe an intriguing correlation between stellar mass and metallicity gradient, consistent with the "downsizing" galaxy formation picture that more massive galaxies are more evolved into a later phase of disk growth, where they experience more coherent mass assembly at all radii and thus show shallower metallicity gradients. Furthermore, 10% of the metallicity gradients measured in my sample are inverted, which are hard to explain by currently existing hydrodynamical simulations and analytical chemical evolution models. My method can be readily applied to data from future space missions employing grism instruments, e.g., JWST, Euclid, WFIRST, and the Chinese Space Station Telescope. Combined with the continuous input of HST resources, these data will revolutionize our understanding of the chemo-structural evolution of galaxies throughout vast cosmic time.