Corporations and their supply chains have to go through significant changes to become more sustainable as society is pressing for sustainable systems. To this end, it is critical to develop new methodologies to trim away processes and activities that add no value and, thus, derive more sustainable supply chains. Considering the need to have a simple tool that can be used by managers to achieve this goal, in this work, we explore the value stream mapping method (VSM) and extend it to support the design of sustainable supply chains in a more systematic and quantitative way. This work proposes a new generic methodology, called SustainSC-VSM, which allows assessing the supply chain’s performance through a set of realistic indicators. These indicators are designed to identify bottlenecks that hinder sustainable operations development and provide guidelines to achieve that goal by following a lean-driven sustainability approach. SustainSC-VSM was tested and validated through its application to a relevant industrial case study, where operational bottlenecks were pinpointed and potential solutions were identified to seek continuous improvement. Although envisioned to be generic and applicable to all supply chains, the indicators should be selected according to the context in study (e.g., services). SustainSC-VSM aims at being a generic and systematic tool to design future value stream maps to achieve a more sustainable supply chain following a lean-driven sustainability approach, through the use of multi-dimensional and multi-disciplinary indicators to identify and solve the supply chain’s bottlenecks.