An effective chip formation process is significant for an efficient metal-cutting process. Long continuous chips can lead to scratches on the machined surface, increasing the risk to operator safety and stability of the machining process. The use of chip grooves on cutting inserts allows for control of the chip formation and breaking process during machining. The shape of the rake surface and the design of the chip groove also affect the efficiency of the machining process. The article presents the use of 3D imaging to analyze changes in the selected chip groove shapes depending on the cutting depth ap = 0.10, 0.25, and 0.50 mm and the angular location of the cutting insert relative to the machined surface of the workpiece (i.e., major cutting-edge angle K = 60° and K = 90°). The analysis methodology was based on the use of 3D image registration and surface shape modeling. In the analysis based on the 3D imaging presented, the novelty was the adaptation of methods typically used to map and model the terrain surface, which have not been used previously in cutting processes. The evaluation of the shape of the chip groove surface was carried out using, e.g., watershed maps and 3D surface maps. The obtained results indicated a significant influence of the cutting depth and major cutting-edge angle on the surface shape, profile, and length of the chip former; chip groove volume; and the theoretical contact area of the formed chip with the cutting insert. It was observed that for small depths of cut, i.e., ap < 0.25 mm, the chip-curling process may be difficult due to the flattened shape of the rake surface. In addition, the influence of the convexity of the rake surface of the cutting insert on the chip formation process was demonstrated. The results of the experimental research that verified the conclusions are presented. The developed results may be useful in the process of selecting the parameters and conditions of the metal finishing through use of tools with a shaped rake surface.