Incoherent pion photoproduction on the deuteron in the D (1232)-resonance region is investigated with special emphasis on polarization observables. For the elementary pion photoproduction operator an effective Lagrangian model which includes the standard pseudovector Born terms and a resonance contribution from the D (1232)-excitation is used. Our results for the elementary gN →pN reaction are in good agreement with recent experimental data and results of other theoretical calculations. A general analysis of all possible polarization observables for the gd →pNN reaction with polarized photon beam and/or oriented deuteron target is presented. The unpolarized differential cross section, photon asymmetry, vector and tensor target asymmetries are predicted for forthcoming experiments.