The current arsenal of molecular tools for site-directed cleavage of single-stranded DNA (ssDNA) is limited. Here, we describe a method for targeted DNA cleavage that requires only the presence of an A nucleotide at the target position. The procedure involves hybridization of a complementary oligonucleotide probe to the target sequence. The probe is designed to create a deliberate G:A mismatch at the desired position of cleavage. The DNA repair enzyme MutY glycosylase recognizes the mismatch structure and selectively removes the mispaired A from the duplex to create an abasic site in the target strand. Addition of an AP-endonuclease, such as Endonuclease IV, subsequently cleaves the backbone dividing the DNA strand into two fragments. With an appropriate choice of an AP-cleaving enzyme, the 3'- and 5'-ends of the cleaved DNA are suitable to take part in subsequent enzymatic reactions such as priming for polymerization or joining by DNA ligation. We define suitable standard reaction conditions for glycosylase/AP-cleaving enzyme (G/AP) cleavage, and demonstrate the use of the method in an improved scheme for in situ detection using target-primed rolling-circle amplification of padlock probes.