Observations of the 1₁₀-1₀₁ 556.936 GHz transition of ortho-water with the Submillimeter Wave Astronomy Satellite have revealed the presence of widespread emission and absorption by water vapor around the strong submillimeter continuum source Sagittarius B2. An incompletely sampled spectral line map of a region of size 26' × 19' around Sgr B2 reveals three noteworthy features. First, absorption by foreground water vapor is detectable at local standard of rest (LSR) velocities in the range -100 to 0 km s^-1 at almost every observed position. Second, spatially extended emission by water is detectable at LSR velocities in the range 80-120 km s^-1 at almost every observed position. This emission is attributable to the 180 pc molecular ring identified from previous observations of CO. The typical peak antenna temperature of 0.075 K for this component implies a typical water abundance of (1.2-8) × 10^-6 relative to H₂. Third, strong absorption by water is observed within 5' of Sgr B2 at LSR velocities in the range 60-82 km s^-1. An analysis of this absorption yields a HO abundance ~(2-4) × 10^-7 relative to H₂ if the absorbing water vapor is located within the core of Sgr B2 itself, or, alternatively, a water column density of ~(2.5-4) × 10¹⁶ cm^-2 if the water absorption originates in the warm, foreground layer of gas proposed previously as the origin of ammonia absorption observed toward Sgr B2.