Catalyzes the irreversible cleavage of the glycosidic bond in both 5'-methylthioadenosine (MTA) and S-adenosylhomocysteine (SAH/AdoHcy) to adenine and the corresponding thioribose, 5'-methylthioribose and S-ribosylhomocysteine, respectively. Also cleaves 5'-deoxyadenosine, a toxic by-product of radical S-adenosylmethionine (SAM) enzymes, into 5-deoxyribose and adenine