Cancers arise through the acquisition of oncogenic mutations and grow by clonal expansion1,2. Here we reveal that most mutagenic DNA lesions are not resolved into a mutated DNA base pair within a single cell cycle. Instead, DNA lesions segregate, unrepaired, into daughter cells for multiple cell generations, resulting in the chromosome-scale phasing of subsequent mutations. We characterize this process in mutagen-induced mouse liver tumours and show that DNA replication across persisting lesions can produce multiple alternative alleles in successive cell divisions, thereby generating both multiallelic and combinatorial genetic diversity. The phasing of lesions enables accurate measurement of strand-biased repair processes, quantification of oncogenic selection and fine mapping of sister-chromatid-exchange events. Finally, we demonstrate that lesion segregation is a unifying property of exogenous mutagens, including UV light and chemotherapy agents in human cells and tumours, which has profound implications for the evolution and adaptation of cancer genomes.