This study investigated the failure mechanism and load-bearing capacity of ultra-high-performance concrete (UHPC) columns confined with high-strength spiral stirrups under axial compression. Based on tests of 75 specimens, a structural stability analysis method was employed to convert multi-point strain measurements into the normalized generalized strain energy density (E_j,norm). The mutation point (Point U) on the E_j,norm-F_j curve, identified via the Mann–Kendall criterion, was proposed as a novel indicator for structural instability and the practical failure load. Parametric analysis showed that increasing the UHPC compressive strength from 100 MPa to 180 MPa raised the failure load by 63%, while increasing the stirrup volumetric ratio from 0.9% to 2.0% yields a further 7.5% increase in the failure load. In contrast, the yield strength of stirrups exerts a negligible influence on the failure load, as the stirrups do not reach their yield strength at the failure load of the concrete columns. A new predictive model for the failure load was developed, which exhibited excellent agreement with test results (mean ratio = 1.000, standard deviation = 0.046, errors within ±13%). The proposed method provided a reliable and stable approach for evaluating the failure load-bearing capacity of confined UHPC columns. The validated predictive model enabled engineers to determine the failure load of confined UHPC columns through simple calculation rather than expensive experimental testing, reducing project costs by 5–10% through optimized material selection and accelerating design timelines by weeks, thereby making UHPC columns more economically competitive for mainstream infrastructure applications.