Topoisomerase 1 (Top1) incises DNA containing ribonucleotides to generate complex DNA lesions that are resolved by APE2 (Apn2 in yeast). How Apn2 engages and processes this DNA damage is unclear. Here, we report X-ray crystal structures and biochemical analysis of Apn2-DNA complexes to demonstrate how Apn2 frays and cleaves 3′ DNA termini via a wedging mechanism that facilitates 1–6 nucleotide endonucleolytic cleavages. APN2 deletion and DNA-wedge mutant Saccharomyces cerevisiae strains display mutator phenotypes, cell growth defects, and sensitivity to genotoxic stress in a ribonucleotide excision repair (RER)-defective background harboring a high density of Top1-incised ribonucleotides. Our data implicate a wedge-and-cut mechanism underpinning the broad-specificity Apn2 nuclease activity that mitigates mutagenic and genome instability phenotypes caused by Top1 incision at genomic ribonucleotides incorporated by DNA polymerase epsilon.