I will present results from two large spectroscopic campaigns using Gemini North and Gemini South to study two distinct populations of galaxy clusters. GMOS-N nod-and-shuffle observations of a large sample of strong lensing selected galaxy clusters from the Sloan Digital Sky Survey have provided redshifts for strongly lensed galaxies behind dozens of  individual cluster lenses. The spectra are combined with extensive multi-wavelength data to provide new insights into a variety of problems involving both the foreground cluster lenses and the background lensed sources. Additionally, I will discuss the current status of and first results from a large NOAO survey program with GMOS-S to measure robust velocity dispersions of 85 galaxy clusters detected via the Sunyaev Zel'dovich effect with the South Pole Telescope (SPT). The SPT cluster catalog is volume-limited above z > 0.3 and M > 5e14 M_sun; this catalog is the gold standard for providing precision constraints on cosmological parameters through measurement of the growth of structure over cosmic time. Velocity dispersion measurements from GMOS-S will provide and independent mass observable that is sensitive to the total gravitational mass and thereby calibrate the relationship between mass and SZ decrement. The GMOS-S spectra have also yielded several exciting ancillary results, which I will summarize.