Catalysis of the reaction: 8-oxo-7,8-dihydrodeoxyguanosine-triphosphate + H2O = 8-oxo-7,8-dihydrodeoxyguanosine phosphate + diphosphate. 8-oxo-7,8-dihydrodeoxyguanosine-triphosphate, or 8-oxo-dGTP, is the oxidised form of the free guanine nucleotide and can act as a potent mutagenic substrate for DNA synthesis causing transversion mutations. 8-oxo-dGTPase hydrolyses 8-oxo-dGTP to its monophosphate form to prevent the misincorporation of 8-oxo-dGTP into cellular DNA.