The chromosome breakage-fusion-bridge (BFB) cycle is a mutational process that produces gene amplification and genome instability. Signatures of BFB cycles can be observed in cancer genomes alongside chromothripsis, another catastrophic mutational phenomenon. We explain this association by elucidating a mutational cascade that is triggered by a single cell division error-chromosome bridge formation-that rapidly increases genomic complexity. We show that actomyosin forces are required for initial bridge breakage. Chromothripsis accumulates, beginning with aberrant interphase replication of bridge DNA. A subsequent burst of DNA replication in the next mitosis generates extensive DNA damage. During this second cell division, broken bridge chromosomes frequently missegregate and form micronuclei, promoting additional chromothripsis. We propose that iterations of this mutational cascade generate the continuing evolution and subclonal heterogeneity characteristic of many human cancers.