Singles $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,p) and coincidence $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,2p${)}^{14}$N measurements have been made at ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=115 MeV over an extended range of the phase space of the two final-state protons. The coincidence measurements have a missing-mass resolution of 4 MeV. The direct two-nucleon absorption cross section extracted from the data is 58\ifmmode\pm\else\textpm\fi{}8 mb. After corrections for final-state interactions, it was found that the two-nucleon ${\mathrm{\ensuremath{\pi}}}^{+}$+np\ensuremath{\rightarrow}pp process accounts for about 76% of the total absorption cross section, and thus is the dominant absorption mechanism. Evidence for absorption on s-p pairs is seen as a broad bump near 32 MeV of excitation. At backward angles the inclusive $^{16}\mathrm{O}$(${\mathrm{\ensuremath{\pi}}}^{+}$,p) spectra show a distinct absorption peak, an important feature not previously observed. Comparisons of distorted wave impulse approximation calculations to both the coincidence data and inclusive data are presented.