In the context of carbon neutrality and sustainable manufacturing, there is an urgent need for carbon emission accounting in the manufacturing industry, especially in high-energy, low-efficiency, and high-carbon emission manufacturing systems. However, the dynamics and coupling of carbon emissions caused by the multiple characteristics of manufacturing systems increase the challenges of carbon emission accounting. To this end, this research aims to develop a generic methodology to reveal the carbon emission characteristics and implement carbon emission accounting for manufacturing systems, so as to support the lean diagnosis and management of carbon emission hotspots. Firstly, the concept of the “meta-carbon-emission block” consisting of both static and variable carbon emission blocks is proposed to characterize the carbon emission behaviors of each device in various operating states. Then, a data-driven carbon emission accounting approach based on the meta-carbon-emission block is presented to calculate the carbon emission and diagnose the carbon emission hotspots. Finally, a typical manufacturing system, that is, a laser welding system for butt welding of aluminum alloy 6061 with multi-source of the carbon emission, multi-device of the processing system, multi-state of the sub-device, and multi-stage of the production, is conducted to validate the proposed approach, and the results revealed the effectiveness and practicality of this approach. This research provides an appropriate theoretical and methodological basis for carbon emission accounting of manufacturing systems and also supports the diagnosis and reduction of carbon emissions for manufacturing industries.