Every cancer originates from a single cell. During expansion of the neoplastic cell population, individual cells acquire genetic and phenotypic differences from each other. Here, to investigate the nature and extent of intra-tumour diversification, we characterized organoids derived from multiple single cells from three colorectal cancers as well as from adjacent normal intestinal crypts. Colorectal cancer cells showed extensive mutational diversification and carried several times more somatic mutations than normal colorectal cells. Most mutations were acquired during the final dominant clonal expansion of the cancer and resulted from mutational processes that are absent from normal colorectal cells. Intra-tumour diversification of DNA methylation and transcriptome states also occurred; these alterations were cell-autonomous, stable, and followed the phylogenetic tree of each cancer. There were marked differences in responses to anticancer drugs between even closely related cells of the same tumour. The results indicate that colorectal cancer cells experience substantial increases in somatic mutation rate compared to normal colorectal cells, and that genetic diversification of each cancer is accompanied by pervasive, stable and inherited differences in the biological states of individual cancer cells.