New near- and far-ultraviolet (NUV and FUV) HST spectra of Mrk 231, the nearest quasar known, are combined with ground-based optical spectra to study the remarkable dichotomy between the FUV and NUV-optical spectral regions in this object. The FUV emission-line features are faint, broad, and highly blueshifted (up to ~7000 km/s), with no significant accompanying absorption. In contrast, the profiles of the NUV absorption features resemble those of the optical Na I D, He I, and Ca II H and K lines, exhibiting broad blue-shifted troughs that overlap in velocity space with the FUV emission-line features and indicate a dusty, high-density and patchy broad absorption line (BAL) screen covering ~90% of the observed continuum source at a distance less than ~2 - 20 pc. The FUV continuum emission does not show the presence of any obvious stellar features and is remarkably flat compared with the steeply declining NUV continuum. The NUV (FUV) features and continuum emission have not varied significantly over the past ~22 (3) years and are unresolved on scales ~40 (170) pc. These results favor an AGN origin for the NUV - FUV line and continuum emission. The observed FUV line emission is produced in the outflowing BAL cloud system, while the Balmer lines arise primarily from the standard broad line region seen through the dusty BAL screen. Our data are inconsistent with the recently proposed binary black hole model. We argue instead that Mrk~231 is the nearest example of weak-lined wind-dominated quasars with high Eddington ratios and geometrically thick (slim) accretion disks; these quasars are likely more common in the early universe.