Tumor genomes abound with mutations, including homozygous gene deletions, suggesting that tumors are robust to genetic perturbation. In model organisms and cancer cell lines, paralogs have been shown to contribute substantially to genetic robustness – they are generally more dispensable for growth than singletons. Here, by analyzing copy number profiles of >10,000 tumors, we test the hypothesis that the increased dispensability of paralogs shapes tumor genome evolution. We find that paralogs are more likely to be homozygously deleted and that this cannot be explained by other factors known to influence copy number variation. Furthermore, features that influence paralog dispensability in cancer cell lines correlate with paralog deletion frequency in tumors. Finally, paralogs that are broadly essential in cancer cell lines are less frequently deleted in tumors than non-essential paralogs. Overall our results suggest that homozygous deletions of paralogs are more frequently observed in tumor genomes because paralogs are more dispensable.