We isolated and analyzed, at single-nucleotide resolution, cancer-associated neochromosomes from well- and/or dedifferentiated liposarcomas. Neochromosomes, which can exceed 600 Mb in size, initially arise as circular structures following chromothripsis involving chromosome 12. The core of the neochromosome is amplified, rearranged, and corroded through hundreds of breakage-fusion-bridge cycles. Under selective pressure, amplified oncogenes are overexpressed, while coamplified passenger genes may be silenced epigenetically. New material may be captured during punctuated chromothriptic events. Centromeric corrosion leads to crisis, which is resolved through neocentromere formation or native centromere capture. Finally, amplification terminates, and the neochromosome core is stabilized in linear form by telomere capture. This study investigates the dynamic mutational processes underlying the life history of a special form of cancer mutation.