In this paper, we show that there is a strong correlation between the strength differential (SD) effects in the plastic flow of the matrix, which arise from its dependence on the third stress invariant, void evolution, and ultimately the ductility of porous metallic polycrystals. For this purpose, detailed micromechanical finite-element analyses of three-dimensional unit cells are carried out. The plastic flow of the matrix is described by a criterion that accounts for strength-differential effects induced by shear deformation mechanisms of the constituent grains through a macroscopic parameter, k; only if there is no SD, k is zero, and the von Mises criterion is recovered. Numerical analyses are conducted for macroscopic proportional tensile loadings corresponding to fixed values of the stress triaxiality (ratio of the mean stress to the second stress invariant). It is shown that for the same macroscopic loading, the local plastic strains and the local stress distribution are strongly dependent on the sign of the parameter k. This in turn has a huge impact on damage accumulation, and ultimately affects the ductility of the porous polycrystals. Specifically, for axisymmetric loadings at third stress invariant positive, the rate of void growth is the slowest in the material with k negative, while the reverse holds true for equibiaxial tension (third stress invariant negative). Consequently, the ductility in axisymmetric tension at third-stress invariant positive is also markedly different from that in equibiaxial tension (third-stress invariant negative).