The def-TZVP and def2-TZVP basis sets are all-electron basis sets, so you probably should not use them together with ECP:s. If you really want to use ECP for Cu, the ecp-10-mdf ECP has a corresponding valence basis set, also called ecp-10-mdf. Looking at the (8s7p6d)/[6s5p3d] ecp-10-mdf basis set, it seems to be of triple-zeta quality. However, I cannot say how efficiently it has been optimized. You can check the original publication for more details (M. Dolg, U. Wedig, H. Stoll, H. Preuss, J. Chem. Phys. 86, 866 (1987)).
Unless you are using ECP with Cu for some very special reason, I'd recommend the all-electron def-TZVP or def2-TZVP basis sets for Cu. The relativistic effects are not usually that important for Cu, and as the ECP only replaces 10 core electrons, the number of basis functions is not decreased significantly. The availability of the RI auxilliary basis sets is another important point. The ecp-10-mdf has a corresponding RI auxbasis set for RI-DFT-calculations, but I did not find a RI-MP2 auxbasis for it.