Cross sections for the incoherent pion photoproduction reaction on the deuteron including final-state interaction effects are studied in the photon energy region from $300$ to $500$ MeV. For the elementary pion photoproduction operator on the free nucleon, the unitary isobar MAID2007 model is used. The interactions in the final two-body subsystems are taken from separable representations of realistic potentials. Numerical results for the unpolarized differential and total cross sections as well as for the doubly polarized differential and total cross sections for parallel and antiparallel helicity states of photon and deuteron for the $\gamma d \to \pi^- pp$, $\gamma d \to \pi^+ nn$, and $\gamma d \to \pi^0 np$ channels are given. Effects of final-state interaction are investigated and their role in these cross sections are found to be significant, specially for $\pi^0$ production.