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The photocatalytic O-H dissociation of water absorbed on a rutile TiO(110) surface in ultrahigh vacuum (UHV) is studied with spin-polarized density functional theory and a hybrid exchange-correlation functional (HSE06), treating the excited-state species as excitons with triplet multiplicity. This system is a model for the photocatalytic oxidation of water by TiO in an aqueous medium, which is relevant for the oxygen evolution reaction and photodegradation of organic pollutants. We provide a comprehensive mechanistic picture where the most representative paths correspond to excitonic configurations with the hole located on three- and two-coordinate surface oxygen atoms (O and O). Our picture explains the formation of the species observed experimentally. At near band gap excitation, the O path leads to the generation of hydroxyl anions which diffuse on the surface, without net oxidation. In contrast, free hydroxyl radicals are formed at supra band gap excitation (e.g., 266 nm) from an interfacial exciton that undergoes O-H dissociation. The oxidation efficiency is low because the path associated with the O exciton, which is the most favored one thermodynamically, is unreactive because of a high propensity for charge recombination. Our results are also relevant to understand the reactivity in the liquid phase. We assign the photoluminescence measured for atomically flat TiO(110) surfaces in an aqueous medium to the O exciton, in line with the proposal based on experiments, and we have identified a species derived from the O exciton with an activated O-Ti bond that may be relevant in photocatalytic applications in an aqueous medium.