In micro-machining, when undeformed chip thickness (a) becomes smaller than the size of tool edge radius (r), the cutting edge radius effect arises by transforming the cutting mechanism from concentrated shear deformation into an extrusion-like behaviour. To analyse the edge radius effect, the governing process parameter is identified as the ratio of a/r. With variation of a/r, 'extrusion-like' finishing zone was identified for Brass and Mg alloy by considering the machined surface integrity, µ-chip morphology and machined surface finishing (Ra). Moreover, 'dirt-like' chip formation could be misleading as "no chip formation" at extreme small a/r value due to the inability of human eye to clearly observe such chips. Finally, 'burnishing-like' finishing is identified in the 'narrow a/r zone' by considering the surface integrity and improvement of machined surface roughness profile. This novel study will help to produce superior quality finishing without requiring post processing of the machined surface.