This paper experimentally analyzes the working behavior characteristics of five concrete-filled steel tube (CFST) arch supports in deep roadway based on the numerical shape function (NSF) method and structural stressing state theory. First, the measured strain data are expanded by the NSF method and modeled as generalized strain energy density (GSED) to characterize the stressing state of the supports. Then, one of the supports is taken as an example and the Mann-Kendall (M-K) criterion is adopted to detect the mutation characteristics of the support, which derives the new definition of structural failure load. Correspondingly, the stressing state modes as well as strain and stress fields for the support are proposed to verify their mutation characteristics. Finally, the common and different characteristics of stressing state, damage development and internal forces for different supports are also summarized. The analytical results of the supports explore a new analysis method for underground structures and the unseen knowledge provides a reference to more rational future design.