This study investigates how saturation (ranging from < 3% to > 97%), freezing temperature (25 °C to − 40 °C), freezing duration (0–16 h), and the number of freeze–thaw cycles (0–40) influence basalt’s mechanical properties. Uniaxial compression tests were performed, and damage as well as constitutive models were developed to capture the mechanical response. The results reveal that the critical saturation range for freeze–thaw damage in basalt lies between 50.1% and 76.9%. When the freezing temperature ranges between − 10 °C and − 20 °C or the freezing duration extends up to 4 h, damage to the basalt intensifies significantly. There is a threshold effect of freezing temperature and duration, where further lowering of temperature or prolonged freezing does not increase damage once the rock is fully frozen. The impact of repeated freeze–thaw cycles shows diminishing marginal effects, with the rate of degradation slowing over multiple cycles. The proposed constitutive model accurately reflects basalt’s mechanical response under various freeze–thaw scenarios by using Young’s modulus and secant moduli as damage calibration parameters. These findings offer valuable insights into understanding rock degradation in cold-region engineering applications, providing guidance for design and maintenance strategies to mitigate rock instability and structural failures caused by freeze–thaw processes. The research outcomes are particularly relevant for underground cavern excavation, slope stability assessment, tunnel construction, and other rock engineering projects in regions subject to repeated freezing and thawing events.