We present a full high resolution SPIRE FTS spectrum of the nearby ultraluminous infrared galaxy Mrk 231. In total 25 lines are detected, including CO J = 5–4 through J = 13–12, 7 rotational lines of H2O, 3 of OH+ and one line each of H2O+, CH+, and HF. We find that the excitation of the CO rotational levels up to J = 8 can be accounted for by UV radiation from star formation. However, the approximately flat luminosity distribution of the CO lines over the rotational ladder above J = 8 requires the presence of a separate source of excitation for the highest CO lines. We explore X-ray heating by the accreting supermassive black hole in Mrk 231 as a source of excitation for these lines, and find that it can reproduce the observed luminosities. We also consider a model with dense gas in a strong UV radiation field to produce the highest CO lines, but find that this model strongly overpredicts the hot dust mass in Mrk 231. Our favoured model consists of a star forming disk of radius 560 pc, containing clumps of dense gas exposed to strong UV radiation, dominating the emission of CO lines up to J = 8. X-rays from the accreting supermassive black hole in Mrk 231 dominate the excitation and chemistry of the inner disk out to a radius of 160 pc, consistent with the X-ray power of the AGN in Mrk 231. The extraordinary luminosity of the OH+ and H2O+ lines reveals the signature of X-ray driven excitation and chemistry in this region.