Social enterprises create innovative solutions to address social issues and achieve sustainable development goals (SDGs). This paper examines the innovative social entrepreneurial processes using the theoretical foundation of responsible innovation (i.e., anticipation, reflexivity, inclusion and deliberation, responsiveness, and knowledge management). The data collected from three case study organisations reveals that social enterprises at the initiation stage address only a few SDGs. However, innovation development and implementation processes lead to products and services diversification and geographical expansion which broaden the SDG focus. During this process, enterprises iteratively conduct activities associated with different dimensions of responsible innovation and operate within ethics, values, and rights-based boundaries. Based on these findings, this paper proposes a process model combining SDG literature with responsible innovation. The managerial implications of using responsible innovation perspective to achieve SDGs are also highlighted.