In many plant and animal taxa mutation rates are higher in males than in females. As a result, the evolutionary speed of genes depends on how much time they spend in either sex. Usually, this time differs between genes located on sex chromosomes but not between those on autosomes. Here we present an unusual system with a partially sex-linked inheritance of autosomes: the hemiclonal frog Rana esculenta (E) which is originally a hybrid between the sexual species R. lessonae (L) and R. ridibunda (R). Rana esculenta excludes the L genome prior to meiosis, produces eggs or sperm containing an unrecombined R genome and restores hybridity by mating with R. lessonae (‘hybridogenesis’). Matings between L males and E females result in offspring with an even sex ratio, whereas the reverse combination produces only daughters. The extent of the resulting female bias and the proportion that R alleles have spent in either sex depend on the relative survival (b) and the relative reproductive contribution (a) of E males vs. E females. In this paper, we analyze mathematically how different combinations of a and b influence the sex ratio in R. esculenta populations and, combined with the male/female mutation rate ratio (α), the evolutionary rate of the clonally transmitted R genome. We find that this rate is higher than in an asexual population and lower than in a sexual one. Hence, clonal diversity through new mutations is more easily achievable than in purely asexual species. In contrast, the occurrence and accumulation of deleterious mutations is lower than in a comparable sexual species. We conclude that these intermediate mutation rates improve the ecological and evolutionary potential of hemiclonal organisms, and we draw attention to the implications for the use of microsatellites.