The sheet metalworking industries possess minimal knowledge in the area of sustainability despite having served as sub-contractors to various industrial sectors. This also highlights that suitable indicators for measuring the sustainability performance of sheet metalworking operations are poorly addressed. As sustainability assessment is regarded as a vital part of sustainable development, this paper has been aimed at establishing a general framework for sustainability assessment of sheet metalworking processes. The main attention was paid to two important processes—the cutting operations with a CNC turret punch press machine and sheet metal bending operations with CNC press brake machine. Stepwise guidelines to implement the proposed framework in sheet metalworking industries are consequently presented. Besides, this study contributes to developing an applicable sustainability indicator set for assessing such manufacturing processes. It makes a valuable contribution to advancing the narrow body of knowledge on the under-researched scope.