Mutation rate is a crucial evolutionary parameter that has typically been treated as a constant in population genetic analyses. However, mutation rate is likely to vary among co-existing individuals within a population, due to genetic polymorphisms, heterogeneous environmental influences, and random physiological fluctuations. We explore the consequences of such mutation rate heterogeneity in a model allowing an arbitrary distribution of mutation rate among individuals, either with or without inheritance. We find that variation of mutation rate about the mean results in a higher probability of producing zero or many simultaneous mutations on a genome. Moreover, it increases the frequency of higher order mutants even under ongoing mutation and selection. We gain a quantitative understanding of how this frequency depends on moments of the mutation rate distribution and selection coefficients. In particular, in a two-locus model, heterogeneity leads to a relative increase in double mutant frequency proportional to the squared coefficient of variation of the mutation rate. Relative effect sizes increase with the number of loci. Finally, this clustering of deleterious mutations into fewer individuals results in a higher population mean fitness. Our results imply that mutation rate heterogeneity allows a population to maintain a higher level of adaptedness to its current environment, while simultaneously harboring greater genetic diversity in the standing variation, which could be crucial for future adaptation to a new environment. Our results also have implications for interpreting mutation rate estimates and mutant frequencies in data.