CTCF/cohesin-binding sites (CBSs) at the chromatin-loop anchors and topologically associating domains are frequently mutated in cancer; however, the underlying molecular mechanisms remain unclear. Here, we investigate whether CTCF and cohesin co-binding on DNA imposes constraints on DNA replication, leading to DNA damage and genomic instability. Our results reveal that CTCF and cohesin remain co-bound to DNA during replication in cancer cells (HeLa). Furthermore, analysis of DNA damage response/repair (DDR) proteins—including MRE11, STN1, γH2AX, and RAD51—showed a high enrichment of these proteins at CBSs, compared with immediate flanking regions. The loss of DDR genes in tumor genomes showed a significant enrichment of somatic mutations at CBSs compared with those tumors with intact DDR genes. Together, we propose that CTCF and cohesin co-binding can impede replication fork progression, leading to DNA damage and DDR activation. However, in cells with defective DDR, these lesions may promote genomic instability at CBSs.