Over the past decade, the significance of sustainable manufacturing has surged dramatically and become a well-known catchphrase. As environmental concerns intensify and resources become scarcer, manufacturing industries have recognized the need to adopt eco-friendly practices urgently. Sustainable manufacturing plays a crucial role in ensuring a harmonious coexistence between industry growth and environmental preservation. In this respect, sustainability assessment based on systems of systems perspective considering triple bottom line simultaneously is an essential strategy. Sustainable manufacturing will not be realized based on name alone or establishing rules. Instead of assessing a manufacturing system as “sustainable” or “unsustainable,” it should be decomposed systematically to find feasible alternative solutions to be more sustainable. Axiomatic Design (AD) theory offering a structured framework enables a systematic breakdown of complex systems into simpler modules while preserving their physical integration and functional independence. This paper presents a comprehensive decomposition of sustainability focusing on manufacturing systems. The European Sustainability Report Standard (ESRS) is considered a basis for knowing customers’ needs and covering the mentioned sustainability metrics. The research results show how an AD-based decomposition can mitigate the complexity and overlaps between sustainability pillars. In addition, it helps manufacturing systems think of other alternatives to push the boundaries of sustainability.