Precision machining is becoming more and more important with the increasing demands on surface quality for various components. This applies, for example, to mirror components in micro-optics or cooling components in microelectronics. Copper is a frequently used material for this purpose, but its mechanical properties make it difficult to machine. In this study, a process strategy for finishing copper surfaces with batch-manufactured micro-grinding tools in an electrochemically assisted grinding process is demonstrated. The tool heads are manufactured from a polyimide-abrasive-suspension and silicon as a carrier substrate using microsystems technology. The matching shafts are milled from aluminium. The tools are then used on pure copper and oxidised copper surfaces. By using finer abrasives grains (1.6–2.4 µm instead of 4–6 µm) than previously, similar surface roughness values could be achieved (Ra = 0.09 ± 0.02 µm, Rz = 1.94 ± 0.73 µm) with the same grinding process. An optimised grinding process that combines the use of rough and fine tools, on the other hand, achieves significantly better surface finishes in just four grinding iterations (Ra = 0.02 ± 0.01 µm, Rz = 0.83 ± 0.21 µm). In order to achieve a further increase in surface quality, this optimised grinding process is combined with the anodic oxidation of the copper workpieces. The surface modification is done to increase the machinability of the surface by creating an oxide layer. This is confirmed by the results of scratch tests carried out, which showed less force acting on the tool during machining with the oxide layer than with a pure copper surface. To realise this within the machine tool, an electrochemical cell is shown that can be integrated into the machine so that the oxidation can be carried out immediately before the grinding process. The copper layers produced inside the electrochemical cell in the machine tool show similar characteristics to the samples produced outside. Processing the oxidised samples with the optimised grinding process led to a further reduction of about 17% in the Rz values (Ra = 0.03 ± 0.01 µm, Rz = 0.69 ± 0.20 µm). The combination of the shown grinding process and the integration of anodic oxidation within the machine tool for the surface modification of copper workpieces seems to be promising to achieve high surface finishes.