Mesoscale ocean eddies dramatically impact oceanic material transport, momentum and energy budgets, and large-scale ocean circulation; therefore, reasonably diagnosing their effects is crucial for providing insights into eddy parameterization scheme development. In this work, a Reynolds and coarse-graining hybrid eddy transport diagnostic framework is proposed and applied in the Southern Ocean. Both the isotropic transport coefficient and anisotropic transport tensor are diagnosed and decomposed into contributions from transient and stationary eddies. The tensor can be split into its symmetric and antisymmetric parts, and the symmetric tensor is further diagonalized to analyze the eigenvalues and eigenvectors. We verify that the anisotropic assumption better fits the ocean mesoscale eddy transport process than the isotropic assumption, at least in the Southern Ocean. We place particular emphasis on the transport tensor’s stationary component affected by large-scale topographies, nonconservative processes, and large-scale flow structures and find that its influence is highly anisotropic horizontally and varies vertically. We probe all tensor-related elements that emerge in our hybrid framework, especially the eigenvalues and eigenvectors of the symmetric tensor. We reveal all three configurations of the major and minor eigenvalues that appear in the Southern Ocean, where the one representing vortex filamentation is the most common scenario. In addition, we discover a high randomness of the eigenvectors, which implies the possibility of a semideterministic and semistochastic anisotropic parameterization scheme.