Deicing salts effectively clear snow and ice from roads by lowering the freezing point of water. However, the salt- freeze-thaw environment significantly degrades asphalt pavement performance and lifespan. Despite this, the mechanical damage properties and crack propagation behaviors of warm-mixed rubber asphalt mixtures remain inadequately understood. To address this, a semi-circular bending test was conducted at a macroscopic level, followed by capturing full-field strain data using Digital Image Correlation (DIC) to examine microscopic failure characteristics and crack propagation patterns. A damage model was then developed based on covariance parameter density to assess the impact of salt-freeze-thaw cycles on warm-mixed rubber asphalt mixtures. The results reveal a notable reduction in the flexural strength and fracture energy of WRA-20, ARA-20, and RA-20 rubber asphalt mixtures after exposure to salt-freeze-thaw cycles. Moreover, crack resistance decreases with higher NaCl solution concentrations during freeze-thaw cycles. Specifically, after 15 freeze-thaw cycles in a 9 % NaCl solution, the flexural strength of these mixtures decreases by 62.19 %, 58.84 % and 72.84 %, respectively, while the fracture energy declines by 50.51 %, 45.48 % and 54.25 %. The covariance parameter density of various asphalt mixtures also decreases with an increasing freeze-thaw cycles, mirroring the trend of the horizontal strain density. Considering 15 freeze-thaw cycles, the horizontal strain density of WRA-20, ARA-20 and RA-20 mixtures decrease by 79.27 %, 82.19 %, and 82.43 % respectively in 9 % NaCl solution. Salt crystallization and ice expansion pressure induce micro-cracks within the mixtures, damaging the internal structure and accelerating strain field evolution under load. Short-term freeze-thaw cycles in high-concentration NaCl solutions produce effects similar to long-term exposure in low-concentration solutions. The salt-freeze-thaw coupling damage model effectively predicts the damage characteristics of interface mechanics for warm-mixed rubber asphalt mixtures. The research results provide a scientific basis for optimizing warm-mixed rubber asphalt mixtures and formulating pavement maintenance strategies in cold regions where deicing salts are commonly used.