The article describes an innovative post-weld surface finishing method, which is characterized by moving a specialized cutting tool along a butt weld. The aforementioned method is unique for the machining allowance, which is treated as the weld bead height and is removed in one step with one pass of the cutting tool. The tool is equipped on one side with linearly arranged tooth-shaped cutting elements, with the adjacent teeth height changing and increasing according to the direction of the feed. The non-standard geometry of the cutting tool enables the finishing of a heterogeneous post-weld surface with increased hardness. The results of studying the 2D profile parameters and the 3D stereometric characteristics of the surface roughness using the optical method are presented in the article. Test samples were made of S235JR steel and butt welded with the MMA, MIG, and TIG methods. Subsequently, the welding bead was ground and finished in accordance with the innovative method to flush the bead and the base metal’s surface. Additionally, residual stress analyses were performed using the X-ray diffraction method in the surface layers of the test samples. Based on the conducted research, the influence of the innovative finishing method on the surface quality is described.