Ion dissociation of H2O2+ following the radiationless decay of core-excited H2O is studied theoretically. The detailed mechanisms of the ion dissociation are discussed by using potential energy diagrams for various electronic states of H2O2+ depicted as a function of the internuclear distance of OH and the bending angle of HOH. The dynamics of the ion dissociation is categorized into three types depending on the site where positive holes of H2O2+ are found. The three types are as follows. (i) One or more positive holes are found on the bonding orbital between O and H. (ii) Two positive holes localize on the oxygen 2p orbital (i.e., the lone-paired electrons on the oxygen atom are ejected). (iii) Two positive holes are present on the oxygen 2p orbital and one more hole appears by shake-up excitation. In the case of (i), H2O2+ easily dissociates by the force of Coulomb repulsion between OH+ and H+. A few lowest electronic states of H2O2+ belong to the type (ii). These low-lying potential curves are less steep than those of the type (i) because Coulomb repulsion does not work. Moreover, such potential energy curves have a shallow well. Reflecting these characteristic features, the ion dissociation is relatively depressed. These results are qualitatively in good accord with the experimental observation. In the case of (iii), it is found that a new two-step ion dissociation process of OH2+--> O++H+ following H2O2+--> H+OH2+ possibly occurs.