The high-temperature rotating structures (HTRS), e.g., steam turbine rotors, often operate in extremely harsh environments with a flexible load condition during peak shaving of power system. In this work, a damage-driven framework for reliability assessment is developed in terms of the cumulative damage-damage threshold interference (CD-DT) principle, in which the cumulative damage and damage threshold are regarded as two random parameters to address uncertainties. The CD-DT principle is founded on the engineering damage theory and incorporates physics-of-failure into the probabilistic modeling of high-temperature structural reliability. Probabilistic damage analysis, correlation analysis of weak sites, system-level reliability analysis, and sensitivity analysis have been encompassed in this framework. Three numerical examples are used to verify the effectiveness and applicability of the proposed framework. Application to steam turbine rotor involving multiple weak sites with multi-damage modes illustrate the implementation procedures of the framework. Results show that the reliability-based design life of rotor decreases with the increases of start-stop frequency, the implementation of a two-shift operation would pose a threat to meeting the safety requirement of a 30-year design life. Furthermore, sensitivity analysis highlights the critical influences of initial rotor temperature and speed rising rate on rotor reliability, providing insights for operational maintenance and reliability optimization.