  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 $\text{CaOH}^+$ molecular ions
co-trapped in $\text{Ca}^+$ ion crystals using a femtosecond laser system. We
report the photodissociation cross section spectra of $\text{CaOH}^+$ for
single-photon processes at $\lambda=$245 - 275$\,$nm and for two-photon
processes at $\lambda=$500 - 540$\,$nm. Measurements are interpreted with
quantum-chemical calculations, which predict the photodissociation threshold
for $\text{CaOH}^+\to \text{Ca}^++\text{OH}$ at 265$\,$nm. This result can
serve as a basis for dissociation-based spectroscopy for studying the internal
structure of $\text{CaOH}^+$. The result also gives a prescription for
recycling $\text{Ca}^+$ ions in large-scale trapped $\text{Ca}^+$ quantum
experiments from undesired $\text{CaOH}^+$ ions formed in the presence of
background water vapor.
