One of the major DNA interstrand cross-link (ICL) repair pathways in mammalian cells is coupled to replication, but the mechanistic roles of the critical factors involved remain largely elusive. Here, we show that purified human SNM1A (hSNM1A), which exhibits a 5′–3′ exonuclease activity, can load from a single DNA nick and digest past an ICL on its substrate strand. hSNM1A-depleted cells are ICL-sensitive and accumulate replication-associated DNA double-strand breaks (DSBs), akin to ERCC1-depleted cells. These DSBs are Mus81-induced, indicating that replication fork cleavage by Mus81 results from the failure of the hSNM1A- and XPF–ERCC1-dependent ICL repair pathway. Our results reveal how collaboration between hSNM1A and XPF–ERCC1 is necessary to initiate ICL repair in replicating human cells.