Density functional theory methods are employed to investigate experimentally proposed mechanisms by which the antitumor drug tirapazamine may react with a DNA sugar-C-1' radical to give the sugar derivative deoxyribonolactone, with concomitant DNA strand breakage. For the previously proposed minor pathway, ionization of the sugar-C-1' radical by tirapazamine, the calculated ionization energy, and the electron affinity of the models of the sugar-C-1' radical of DNA and tirapazamine suggest that tirapazamine must be protonated to be able to oxidize the sugar-C-1' radical. The preferred mechanism for reaction of tirapazamine with a sugar-C-1' radical, in agreement with experimental observations, is found to proceed by direct attack of an N-oxide oxygen of tirapazamine at the sugar-C-1' position, followed by homolytic cleavage of the N-O bond of the drug moiety. Possible alternative mechanisms are also investigated.