Surface roughness is one of the main quality indicators and often a technical requirement specified for mechanical components, where achieving the proper surface quality is crucial for part functionality. In actual machining, surface roughness is influenced by numerous factors, including cutting parameters, tool variables, and workpiece variables. One of the key factors affecting surface roughness and compliance with specified geometric tolerances is workpiece clamping rigidity. This study evaluates the quality of the machined surface depending on the clamping method of the blank. Surface roughness is compared for components clamped in a universal three-jaw chuck versus a collet chuck, utilizing two types of indexable rhombic cutting inserts: VCGT and VCMT types. The obtained results demonstrate that using a collet chuck stabilizes the cutting process and improves the uniformity of the surface roughness profile of the machined parts.