Folate deprivation drives the instability of a group of rare fragile sites (RFSs) characterized by CGG trinucleotide repeat (TNR) sequences. Pathological expansion of the TNR within the FRAXA locus perturbs DNA replication and is the major causative factor for fragile X syndrome, a sex-linked disorder associated with cognitive impairment. Although folate-sensitive RFSs share many features with common fragile sites (CFSs; which are found in all individuals), they are induced by different stresses and share no sequence similarity. It is known that a pathway (termed MiDAS) is employed to complete the replication of CFSs in early mitosis. This process requires RAD52 and is implicated in generating translocations and copy number changes at CFSs in cancers. However, it is unclear whether RFSs also utilize MiDAS and to what extent the fragility of CFSs and RFSs arises by shared or distinct mechanisms. Here, we demonstrate that MiDAS does occur at FRAXA following folate deprivation but proceeds via a pathway that shows some mechanistic differences from that at CFSs, being dependent on RAD51, SLX1, and POLD3. A failure to complete MiDAS at FRAXA leads to severe locus instability and missegregation in mitosis. We propose that break-induced DNA replication is required for the replication of FRAXA under folate stress and define a cellular function for human SLX1. These findings provide insights into how folate deprivation drives instability in the human genome.