This study determines topological cross sections and rescattering effects for 200-GeV/c $\mathrm{pd}$ interactions observed in a 60 000-picture exposure of the Fermilab 30-inch deuterium bubble chamber. We measure the $\mathrm{pd}$ inelastic cross section for ${n}_{\mathrm{ch}}\ensuremath{\ge}3$ to be 55.0\ifmmode\pm\else\textpm\fi{}0.8 mb and find that (17.4\ifmmode\pm\else\textpm\fi{}1.8)% of the $\mathrm{pn}$ events have a secondary interaction with the spectator proton. The rescattering is adequately described by a model which assumes the rescattering probability to be independent of the primary collision multiplicity. The multiplicity distribution for nonrescattered $\mathrm{pn}$ interactions has $〈n〉=7.3\ifmmode\pm\else\textpm\fi{}0.1$ and ${f}_{2}^{\mathrm{cc}}=8.4\ifmmode\pm\else\textpm\fi{}0.5$.