Single point incremental forming (SPIF) is a sheet metal forming process in which a simple cylindrical tool with a pre-defined tool path is used to deform the sheet plastically by applying the localized deformation progressively. SPIF has been considered as a flexible process; as it does not require any specialized tool/dies; hence, this flexible process is widely used in biomedical, automobile, and aerospace industries. In the present work, the effect of SPIF process parameters (such as step size, spindle speed, and feed rate) on the average surface roughness (Ra) on thin sheets of Inconel 625 super alloy is examined. The Inconel 625 is incrementally deformed according to the Taguchi design of experiment (orthogonal array L9). Later, to understand the wear mechanism, the formed surface morphology was studied using an optical microscope. The ANOVA analysis is also performed to identify the most influencing factor on average surface roughness (Ra). The experimental and statistical results exhibit that the average surface roughness/surface quality is greatly affected by step size followed by feed rate and spindle speed in decreasing order. The main effect plots for mean and S/N ratio show that for minimum surface roughness or better surface quality, the optimum level of parameters is found as low step size (0.10 mm), medium feed rate (350 mm/min), and low spindle speed (200 rpm), respectively. ANOVA analysis shows that the process parameters step size and feed rate had only physical significance but not statistical significance on surface roughness. At a higher level of forming process parameters, due to huge frictional heat at the tool-thin sheet interface, the adhesive wear of thin sheets took place, which increased the surface roughness of the Inconel 625 sheet.