Molecular ions that are generated by chemical reactions with trapped atomic ions can serve as an accessible testbed for developing molecular quantum technologies. On the other hand, they are also a hindrance to scaling up quantum computers based on atomic ions as unavoidable reactions with background gas destroy the information carriers. Here, we investigate the single- and two-photon dissociation processes of single CaOH+ molecular ions co-trapped in Ca+ ion crystals using a femtosecond laser system. We report the photodissociation cross section spectra of CaOH+ for single-photon processes at λ=245 - 275nm and for two-photon processes at λ=500 - 540nm. Measurements are interpreted with quantum-chemical calculations, which predict the photodissociation threshold for CaOH+→Ca++OH at 265nm. This result can serve as a basis for dissociation-based spectroscopy for studying the internal structure of CaOH+. The result also gives a prescription for recycling Ca+ ions in large-scale trapped Ca+ quantum experiments from undesired CaOH+ ions formed in the presence of background water vapor.