Human cancers are frequently polyploid, containing multiple aneuploid subpopulations that differ in total DNA content. In this study we exploit this property to reconstruct evolutionary histories, by assuming that mutational complexity increases with time. We developed an experimental method called Ploidy-Seq that uses flow-sorting to isolate and enrich subpopulations with different ploidy prior to next-generation genome sequencing. We applied Ploidy-Seq to a patient with a triple-negative (ER-/PR-/HER2-) ductal carcinoma and performed whole-genome sequencing to trace the evolution of point mutations, indels, copy number aberrations, and structural variants in three clonal subpopulations during tumor growth. Our data show that few mutations (8% to 22%) were shared between all three subpopulations, and that the most aggressive clones comprised a minority of the tumor mass. We expect that Ploidy-Seq will have broad applications for delineating clonal diversity and investigating genome evolution in many human cancers.