In this first paper on the results of our Herschel PACS survey of local Ultraluminous Infrared Galaxies (ULIRGs), as part of our SHINING survey of local galaxies, we present far-infrared spectroscopy of Mrk 231, the most luminous of the local ULIRGs, and a type 1 broad absorption line AGN. For the first time in a ULIRG, all observed far-infrared fine-structure lines in the PACS range were detected and all were found to be deficient relative to the far infrared luminosity by 1 - 2 orders of magnitude compared with lower luminosity galaxies. The deficits are similar to those for the mid-infrared lines, with the most deficient lines showing high ionization potentials. Aged starbursts may account for part of the deficits, but partial covering of the highest excitation AGN powered regions may explain the remaining line deficits. A massive molecular outflow, discovered in OH and 18OH, showing outflow velocities out to at least 1400 km/sec, is a unique signature of the clearing out of the molecular disk that formed by dissipative collapse during the merger. The outflow is characterized by extremely high ratios of 18O / 16O suggestive of interstellar medium processing by advanced starbursts.