Polyploid cells result in aneuploidy through aberrant chromosome segregation, possibly leading to tumorigenesis. Although polyploid cells are induced through over-replication by a variety of agents, including DNA-damaging drugs, the mechanisms that induce polyploidy have been hitherto unknown. Here, we show that treatment with bleomycin, a glycopeptide anticancer drug, induces over-replication at low cytotoxic doses. During bleomycin-induced over-replication, mitotic entry is inhibited through tyrosine phosphorylation of CDK1 along the ATM/ATR pathway in the early phase of treatment. Bleomycin-induced over-replication is inhibited by the inhibitors of the ATM/ATR pathway through abrogation of bleomycin-induced G2 arrest, and the ATM/ATR inhibitors promote cell death instead of over-replication. Following the phosphorylation of CDK1, the level of cyclin B1 is decreased in the late phase of treatment. Time-lapse imaging of clone cells that express a live cell marker of endogenous cyclin B1 revealed that cyclin B1 is degraded in G2-arrested cells upon bleomycin treatment. Our findings lead to a model of how the ATM/ATR pathway acts as a molecular switch for regulating cell fates, flipping between cell death via progress into mitosis, and over-replication via sustained G2 arrest upon DNA damage, where cyclin B1 degradation is an important factor for inducing over-replication.