We present interferometric observations of the CN(1–0) line emission in Mrk 231 and combine them with previous observations of CO and other H₂ gas tracers to study the physical properties of the massive molecular outflow. We find a strong boost of the CN/CO(1–0) line luminosity ratio in the outflow of Mrk 231, which is unprecedented compared to any other known Galactic or extragalactic astronomical source. For the dense gas phase in the outflow traced by the HCN and CN emissions, we infer X_CN ≡ [CN]/[H₂]> X_HCN by at least a factor of three, with H₂ gas densities of n_H2 ∼ 10⁵⁻⁶ cm⁻³. In addition, we resolve for the first time narrow spectral features in the HCN(1–0) and HCO⁺(1–0) high-velocity line wings tracing the dense phase of the outflow. The velocity dispersions of these spectral features, σ_v ∼ 7−20 km s⁻¹, are consistent with those of massive extragalactic giant molecular clouds detected in nearby starburst nuclei. The H₂ gas masses inferred from the HCN data are quite high, M_mol ∼ 0.3−5 × 10⁸ M_⊙. Our results suggest that massive complexes of denser molecular gas survive embedded into the more diffuse H₂ phase of the outflow, and that the chemistry of these outflowing dense clouds is strongly affected by UV radiation.