We report the detection of a massive neutral gas outflow in the z = 2.09 gravitationally lensed dusty star-forming galaxy HATLAS J085358.9+015537 (G09v1.40), seen in absorption with the OH+(11-10) transition using spatially resolved (0"5 × 0"4) Atacama Large Millimeter/submillimeter Array (ALMA) observations. The blueshifted OH+ line is observed simultaneously with the CO(9-8) emission line and underlying dust continuum. These data are complemented by high-angular-resolution (0"17 × 0"13) ALMA observations of CH+(1-0) and underlying dust continuum, and Keck 2.2 μm imaging tracing the stellar emission. The neutral outflow, dust, dense molecular gas, and stars all show spatial offsets from each other. The total atomic gas mass of the observed outflow is 6.7 × 109M⊙, >25% as massive as the gas mass of the galaxy. We find that a conical outflow geometry best describes the OH+ kinematics and morphology and derive deprojected outflow properties as functions of possible inclination (0°.38-64°). The neutral gas mass outflow rate is between 83 and 25,400 M⊙ yr-1, exceeding the star formation rate (788 ± 300M⊙ yr-1) if the inclination is >3°.6 (mass-loading factor = 0.3-4.7). Kinetic energy and momentum fluxes span (4.4-290) × 109 L⊙ and (0.1-3.7) × 1037 dyne, respectively (energy-loading factor = 0.013-16), indicating that the feedback mechanisms required to drive the outflow depend on the inclination assumed. We derive a gas depletion time between 29 and 1 Myr, but find that the neutral outflow is likely to remain bound to the galaxy unless the inclination is small and may be reaccreted if additional feedback processes do not occur.