Limit state analysis provides building designers with a better understanding of fundamental structural resistance and deformation requirements, resulting in an overall material economy and offering clear safety boundary conditions for intelligent structural design. Cold-formed high-strength steel has extensive application prospects in structural engineering due to its excellent mechanical properties and flexible cross-sectional options. However, most existing research focuses on its ultimate strength-related behavior, lacking sufficient investigation into deformation properties. This study aims to comprehensively reveal the continuous variation laws of structural resistance and ductility of cold-formed high-strength CHSs (circular hollow sections) with different cross-sectional selections under axial load. Through reliable finite element analysis, the effects of yield strength (f_sy) of cold-formed CHSs, diameter-to-thickness ratio (D/t), and cross-sectional slenderness (λ) on compressive performance in the limit state, including failure mode, axial load-end shortening curve, ultimate-to-yield strength ratio (N_u/N_y), and ductility indicators (displacement ductility coefficient (μ) corresponding to the ascending stage and post-buckling ductility degradation coefficient (R_0.85)), were systematically investigated. The results indicate that the dominant failure mode of high-strength CHSs exhibits outward deformation. With an increase of f_sy and D/t, the value of N_u/N_y decreases, and the development of multiple compression performance exhibits significant nonlinearity, which indicates that blindly improving material strength may not necessarily be conducive to developing structural compressive performance or achieving efficient and economical design solutions. To better serve the ductile limit design of high-strength CHSs, combined with available experimental data and simulation results, the upper limit of λ is proposed to be 0.22, and the predictive models of μ and R_0.85 are established, respectively.