Catalysis of the removal of oxidized purine bases by cleaving the N-C1' glycosidic bond between the oxidized purine and the deoxyribose sugar. The reaction involves the formation of a covalent enzyme-substrate intermediate. Release of the enzyme and free base by a beta-elimination or a beta, gamma-elimination mechanism results in the cleavage of the DNA backbone 3' of the apurinic (AP) site.