The industrial cloud robotics (ICRs) integrates distributed industrial robot resources in various places to support complex task processing for multi-resource service requirements, and manufacturing capability assessment is the key link in determining the optimal service composition to realize the value-added of ICRs resources. However, the traditional evaluation method ignores the positive and negative cooperative effects of the manufacturing capability correlation among the robot individuals on the overall manufacturing capability of the ICRs composition. In addition, the problems of excessive resource consumption and serious environmental pollution in the manufacturing industry are becoming increasingly serious. The paper proposes a dynamic assessment method of sustainable manufacturing capability for ICRs based on the correlation relationship to solve above problems. Firstly, an extensible multi-dimensional indicator system of sustainable manufacturing capability is constructed. Then, multiple composition correlation relationships among ICRs are analyzed to establish the correlation assessment model. Furthermore, a set of dynamic evaluation methods is proposed, in which the evaluation indicators raw data is processed based on the service correlation model and the traditional network analytic network process method is improved based on the data correlation model. Finally, a case study is implemented to show the reasonability and effectiveness of the proposed method in assessment of sustainable manufacturing capability for ICRs.