DNA replication is a highly coordinated cell cycle process that can become dysregulated in cancer, increasing both proliferation and mutation rates. Single-cell whole genome sequencing holds potential for studying replication dynamics of cancer cells; however, computational methods for identifying S-phase cells and inferring single-cell replication timing profiles remain immature for samples with heterogeneous copy number. Here we report a new method, PERT, which jointly infers replication and somatic copy number states of S-phase cells. This method enabled us to analyze the replication dynamics of >10,000 S-phase single-cell genomes across various triple negative breast cancers and cell lines with subclonal copy number heterogeneity. We show that PERT robustly predicts cell cycle phase, quantifies replication timing variability, and approximates relative proliferation rates between tumor subclones. Our results illuminate how aberrant DNA replication processes can both drive and result from evolution of human tumors.