A remarkable observation emerging from recent cancer genome analyses is the identification of chromothripsis as a one-off genomic catastrophe, resulting in massive somatic DNA structural rearrangements (SRs). Largely due to lack of suitable model systems, the mechanistic basis of chromothripsis has remained elusive. We developed an integrative method termed "complex alterations after selection and transformation (CAST)," enabling efficient in vitro generation of complex DNA rearrangements including chromothripsis, using cell perturbations coupled with a strong selection barrier followed by massively parallel sequencing. We employed this methodology to characterize catastrophic SR formation processes, their temporal sequence, and their impact on gene expression and cell division. Our in vitro system uncovered a propensity of chromothripsis to occur in cells with damaged telomeres, and in particular in hyperploid cells. Analysis of primary medulloblastoma cancer genomes verified the link between hyperploidy and chromothripsis in vivo. CAST provides the foundation for mechanistic dissection of complex DNA rearrangement processes.