Interstrand DNA-DNA cross-links (ICLs) are generated by endogenous processes, drugs, and environmental toxins. Understanding the cellular pathways by which various ICLs are repaired is critical to understanding their biological effects. Recent studies showed that replication-dependent repair of an ICL derived from the reaction of an abasic (AP) site with an adenine residue (dA) on the opposing strand of duplex DNA proceeds via a novel mechanism in which the DNA glycosylase NEIL3 unhooks the ICL. Here we examined the ability of the glycosylase domain of murine NEIL3 (MmuNEIL3-GD) to unhook dA-AP ICLs. The enzyme selectively unhooks the dA-AP ICL located at the duplex/single-strand junction of splayed duplexes that model the strand-separated DNA at the leading edge of a replication fork. We show that the ability to unhook the dA-AP ICL is a specialized function of NEIL3 as this activity is not observed in other BER enzymes. Importantly, NEIL3 only unhooks the dA-AP ICL when the AP residue is located on what would be the leading template strand of a model replication fork. The same specificity for the leading template strand was observed with a 5,6-dihydrothymine monoadduct, demonstrating that this preference is a general feature of the glycosylase and independent of the type of DNA damage. Overall, the results show that the glycosylase domain of NEIL3, lacking the C-terminal NPL4 and GRF zinc finger motifs, is competent to unhook the dA-AP ICL in splayed substrates and independently enforces important substrate preferences on the repair process.