Clonal genome evolution is a key feature of asexually reproducing species and human cancer development. While many studies have described the landscapes of clonal genome evolution in cancer, few determine the underlying evolutionary parameters from molecular data, and even fewer integrate theory with data. We derived theoretical results linking mutation rate, time, expansion dynamics, and biological/clinical parameters. Subsequently, we inferred time-resolved estimates of evolutionary parameters from mutation accumulation, mutational signatures and selection. We then applied this framework to predict the time of speciation of the marbled crayfish, an enigmatic, globally invasive parthenogenetic freshwater crayfish. The results predict that speciation occurred between 1986 and 1990, which is consistent with biological records. We also used our framework to analyze whole-genome sequencing datasets from primary and relapsed glioblastoma, an aggressive brain tumor. The results identified evolutionary subgroups and showed that tumor cell survival could be inferred from genomic data that was generated during the resection of the primary tumor. In conclusion, our framework allowed a time-resolved, integrated analysis of key parameters in clonally evolving genomes, and provided novel insights into the evolutionary age of marbled crayfish and the progression of glioblastoma.