Cancer genomes exhibit surprisingly weak signatures of negative selection. This may be because tumors evolve under weak selective pressures (‘weak selection’) or because genome-wide linkage in cancer prevents most deleterious mutations from being removed due to Hill-Robertson interference3 (‘inefficient selection’). The weak selection model argues that most genes are only important for multicellular function and that selection acts only on a subset of essential genes. In contrast, the inefficient selection model predicts that only cancers with low mutational burdens, where linkage effects are minimal, will exhibit strong signals of negative selection against deleterious passengers and positive selection for beneficial drivers. We leverage the 10,000-fold variation in mutational burden across cancer subtypes to stratify tumors by their genome-wide mutational burden and used a normalized ratio of nonsynonymous to synonymous substitutions (dN/dS) to quantify the extent that selection varies with mutation rate. We find that appreciable negative selection (dN/dS ~ 0.4) is present in tumors with a low mutational burden, while the remaining cancers (96%) exhibit dN/dS ratios approaching 1, suggesting that the majority of tumors do not remove deleterious passengers. A parallel pattern is seen in drivers, where positive selection attenuates as the mutational burden of cancers increases. Both trends persist across tumor-types, are not exclusive to essential or housekeeping genes, are present in clonal and subclonal mutations, and persist in Copy Number Alterations. A consequence of this inability to remove deleterious passengers is that tumors with elevated mutational burdens, which are expected to harbor substantial protein folding stress, upregulate heat shock pathways. Finally, using evolutionary modeling, we find that Hill-Robertson interference alone can reproduce the patterns of attenuated selection observed in both drivers and passengers if the average fitness cost of passengers is 1.0% and the average fitness benefit of drivers is 19%. As a result, despite the weak individual fitness effects of passengers, most cancers harbor a large mutational load (median ~40% total fitness cost). Collectively, our findings suggest that the lack of observed negative selection in most tumors is not due to relaxed selective pressures, but rather the inability of selection to remove individual deleterious mutations in the presence of genome-wide linkage.