The evolution of dispersal during range expansion increases invasion speed, provided that a species can adapt sufficiently fast to novel local conditions. Iterated founder effects during range expansion, however, cause low levels of local genetic diversity at these range margins. Mutation rates can evolve, too, under conditions that favor an increased rate of local adaptation, but this has thus far only been associated with asexual populations. As selection acts on the mutation that occurs at a gene under selection and not on the rate with which such mutations occur, the evolution of mutation rates is the result of indirect selection. The establishment of a particular mutation rate is thus restricted to genetic hitchhiking, which is highly sensitive to recombination. However, under conditions of genetic similarity, typical for expanding range margins, the evolution of mutation rates in sexual populations might be possible. Using an individual-based model we show that natural selection leads to co-evolution of dispersal rates and mutation rates in sexual populations due to spatial sorting. The evolution of mutation rate is adaptive and clearly advances range expansion both through its effect on the evolution of dispersal rate, and the evolution of local adaptation. By this we extend the existing theory on the evolution of mutation rates, which was thought to be limited to asexual populations, with possibly far-reaching consequences concerning invasiveness and the rate at which species can adapt to novel environmental conditions.