Sex and recombination are pervasive throughout nature despite their substantial costs. Understanding the evolutionary forces that maintain these phenomena is a central challenge in biology. One longstanding hypothesis argues that sex is beneficial because recombination speeds adaptation. Theory has proposed several distinct population genetic mechanisms that could underlie this advantage. For example, sex can promote the fixation of beneficial mutations either by alleviating interference competition (the Fisher-Muller effect) or by separating them from deleterious load (the ruby in the rubbish effect). Previous experiments confirm that sex can increase the rate of adaptation, but these studies did not observe the evolutionary dynamics that drive this effect at the genomic level. Here we present the first, to our knowledge, comparison between the sequence-level dynamics of adaptation in experimental sexual and asexual Saccharomyces cerevisiae populations, which allows us to identify the specific mechanisms by which sex speeds adaptation. We find that sex alters the molecular signatures of evolution by changing the spectrum of mutations that fix, and confirm theoretical predictions that it does so by alleviating clonal interference. We also show that substantially deleterious mutations hitchhike to fixation in adapting asexual populations. In contrast, recombination prevents such mutations from fixing. Our results demonstrate that sex both speeds adaptation and alters its molecular signature by allowing natural selection to more efficiently sort beneficial from deleterious mutations.