Obtaining a complete census of cosmic star formation requires an understanding of the faint star-forming galaxies that are beyond the detection limits of our current surveys. To find these faint galaxies, we use the power of gravitational lensing from foreground massive galaxy clusters to push the detection limits of the Hubble Space Telescope (HST) to much fainter luminosities. Combining very deep ultraviolet, optical and near-IR imaging from HST, with magnification of strong gravitational lensing from three foreground galaxy clusters, we discover a sample of 780 ultra-faint star-forming galaxies at 1 < z < 3. The UV absolute magnitude of these galaxies are extended down to very faint magnitudes of MUV < −12.5 AB mag. Using this unprecedented sample, we study the evolution of the UV luminosity function (LF) between 1 < z < 3. We find that the UV LFs are steep with an estimate of faint-end slopes of α = −1.56±0.04, α = −1.72±0.04 and α = −1.94±0.06 at 1.0 < z < 1.6, 1.6 < z < 2.2 and 2.2 < z < 3.0, respectively. We demonstrate that there is no sign of turnover in these UV LFs at least down to Muv = −14. As an important consequence of steep LFs, we show that the faint star-forming galaxies covered in this study with −18 < Muv < −12.5, produce a majority (55% − 60%) of the unobscured UV luminosity density at 1 < z < 3. Furthermore, we examine two techniques, fitting a power law to broad-band photometry as well as best-fit SED for each object, to study the evolution of rest-frame UV spectral slopes β for these ultra-faint galaxies. We demonstrate that our UV spectral slopes β change with UV luminosity, such that galaxies become bluer at fainter luminosities. However, we show that the UV spectral slope β−Muv correlation is not tight and there is a large intrinsic scatter in the UV slope distribution at a given Muv. Using hydro-dynamical simulations of dwarf galaxies, we demonstrate that the bursty star formation histories alone can explain the intrinsic scatter in β.