Dysregulated DNA replication is both a cause and a consequence of aneuploidy, yet the dynamics of DNA replication in aneuploid cell populations remains understudied. We developed a new method, PERT, for inferring cell-specific DNA replication states from single-cell whole genome sequencing, and investigated clone-specific DNA replication dynamics in >50,000 cells obtained from a collection of aneuploid and clonally heterogeneous cell lines, xenografts and primary cancer tissues. Clone replication timing (RT) profiles correlated with future copy number changes in serially passaged cell lines. Cell type was the strongest determinant of RT heterogeneity, while whole genome doubling and mutational process were associated with accumulation of late S-phase cells and weaker RT associations. Copy number changes affecting chromosome X had striking impact on RT, with loss of the inactive X allele shifting replication earlier, and loss of inactive Xq resulting in reactivation of Xp. Finally, analysis of time series xenografts illustrate how cell cycle distributions approximate clone proliferation, recapitulating expected relationships between proliferation and fitness in treatment-naive and chemotherapeutic contexts.