Mutations in genes involved in DNA replication, such as flap endonuclease 1 (FEN1), can cause single-stranded DNA breaks (SSBs) and subsequent collapse of DNA replication forks leading to DNA replication stresses. Persistent replication stresses normally induce p53-mediated senescence or apoptosis to prevent tumour progression. It is unclear how some mutant cells can overcome persistent replication stresses and bypass the p53-mediated pathways to develop malignancy. Here we show that polyploidy, which is often observed in human cancers, leads to overexpression of BRCA1, p19arf and other DNA repair genes in FEN1 mutant cells. This overexpression triggers SSB repair and non-homologous end-joining pathways to increase DNA repair activity, but at the cost of frequent chromosomal translocations. Meanwhile, DNA methylation silences p53 target genes to bypass the p53-mediated senescence and apoptosis. These molecular changes rewire DNA damage response and repair gene networks in polyploid tumour cells, enabling them to escape replication stress-induced senescence barriers.