Antiproton-deuteron (pd) scattering is calculated at beam energies below 300 MeV within the Glauber approach, utilizing the amplitudes of the JülichN N models. A good agreement is obtained with available experimental data on upolarized differential and integrated pd cross sections. Predictions for polarized totalpd cross sections are presented, obtained within the single scattering approximation including Coulomb-nuclear interference effects. It is found that the total longitudinal and transversalpd cross sections are comparable in absolute value to those forpp scattering. The kinetics of polarization buildup is considered.