Using recycled cathode ray tube (CRT) funnel glass as a substitute for sand contributes to both reducing natural aggregate consumption and the disposal of CRT funnel glass. Currently, most studies have focused on the mechanical and durability properties of mortar or concrete containing CRT glass as fine aggregate. However, the study of the dynamic loadings (e.g., earthquake load, wind load and impact load) of major concrete structures containing CRT glass is still limited. In this paper, a dynamic thermo-mechanical analysis test with various frequencies (0.1 Hz–2.0 Hz) and temperatures (−30 °C−30 °C) is undertaken on mortars with different CRT replacement ratios (0, 20%, 40%, 60%, 80%, and 100%). The test results show that the storage modulus (stiffness) of mortar with incorporated CRT glass is lower than that of control mortar in most cases, but the decreasing trend is not proportional to the CRT replacement ratio. However, the presence of CRT glass in the mix has a negligible impact on the frequency dependence of the storage modulus of mortar. The storage modulus of each replacement ratio is nearly constant for all excitation frequencies. The frequency dependence of loss tangent (damping behavior) is significantly improved with CRT glass under 0 °C. This indicates that a frequency dependent damping model is needed when dynamic analysis is conducted on concrete structures with incorporated CRT glass in cold weather.