Cancer is a disease of multicellularity, observed across the tree of life. In principle, animals with larger body sizes and longer lifespans should be at increased risk of developing cancer. However, there is no strong relationship between these traits and cancer across mammals. Previous studies have proposed that increased copy number of cancer-related genes may enhance the robustness of cancer suppression pathways in long-lived mammals, but these studies have not extended beyond known cancer-related genes. In this study, we conducted a phylogenetic generalised least squares (PGLS) analysis to test for associations between copy number of all protein-coding genes and longevity, body size, and cancer prevalence across 94 species of mammals. In addition to investigating the copy number of individual genes, we tested sets of related genes for a relationship between the aggregated gene copy number of the set and these traits. We did not find strong evidence to support the hypothesis that adaptive changes in gene copy number contribute to the lack of correlation between cancer prevalence and body size or lifespan. However, we found several biological processes where aggregate copy number was associated with malignancy rate. The strongest association was for the gene set relating to transforming growth factor-beta (TGF-β), a cytokine that plays a role in cancer progression. Overall, this study provides a comprehensive evaluation of the role of gene copy number in adaptation to body size and lifespan and sheds light on the contribution of gene copy number to variation in cancer prevalence across mammals.