We have obtained deep ultraviolet imaging of the lensing cluster A1689 with the WFC3/UVIS camera onboard the Hubble Space Telescope in the F275W (30 orbits) and F336W (4 orbits) filters. These images are used to identify z ~ 2 star-forming galaxies via their Lyman break, in the same manner that galaxies are typically selected at z >= 3. Because of the unprecedented depth of the images and the large magnification provided by the lensing cluster, we detect galaxies 100× fainter than previous surveys at this redshift. After removing all multiple images, we have 58 galaxies in our sample in the range -19.5 < M 1500 < -13 AB mag. Because the mass distribution of A1689 is well constrained, we are able to calculate the intrinsic sensitivity of the observations as a function of source plane position, allowing for accurate determinations of effective volume as a function of luminosity. We fit the faint-end slope of the luminosity function to be α = -1.74 ± 0.08, which is consistent with the values obtained for 2.5 < z < 6. Notably, there is no turnover in the luminosity function down to M 1500 = -13 AB mag. We fit the UV spectral slopes with photometry from existing Hubble optical imaging. The observed trend of increasingly redder slopes with luminosity at higher redshifts is observed in our sample, but with redder slopes at all luminosities and average reddening of langE(B - V)rang = 0.15 mag. We assume the stars in these galaxies are metal poor (0.2 Z ⊙) compared to their brighter counterparts (Z ⊙), resulting in bluer assumed intrinsic UV slopes and larger derived values for dust extinction. The total UV luminosity density at z ~ 2 is 4.31^{+0.68}_{-0.60} \times 10^{26} erg s-1 Hz-1 Mpc-3, more than 70% of which is emitted by galaxies in the luminosity range of our sample. Finally, we determine the global star formation rate density from UV-selected galaxies at z ~ 2 (assuming a constant dust extinction correction of 4.2 over all luminosities and a Kroupa initial mass function) of 0.148^{+0.023}_{-0.020} M ⊙ yr-1 Mpc-3, significantly higher than previous determinations because of the additional population of fainter galaxies and the larger dust correction factors. Some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation.