In alpine regions, the durability of asphalt pavement is worse due to the harsh climate. However, crumb rubber modified asphalt has the potential to improve the durability of pavement. Based on matrix asphalt, crumb rubber, Trans-Polyoctenamer Rubber Reactive Modifier (TOR), and an orthogonal test, the preparation scheme of crumb rubber modified asphalt suitable for alpine regions was obtained. The crumb rubber was selected 30 mesh, and the content of crumb rubber was 24% of the quality of matrix asphalt. Shearing time was 60 min, and preparation temperature was 205 °C. Shearing rate was 5000 r/min, and optimum TOR content was set as 4.5% of the quality of crumb rubber. The temperature susceptibility of matrix asphalt (JZ), crumb rubber modified asphalt (AR), crumb rubber modified asphalt mixed with TOR (TAR) was investigated. The high temperature performance indexes, including phase angle, the complex modulus index, and rutting factor, and the low temperature performance indexes including creep rate and stiffness modulus, the ratio of creep rate and stiffness modulus, Burgers model parameters, dissipated energy ratio, and the derivative of creep compliance were analyzed in depth with multiple parameters. Meanwhile, the mechanisms of prepared AR and TAR were explored. The results indicate that the PG grading is PG64-22 of JZ, PG70-34 of AR, and PG82-28 of TAR. The deformation resistance of TAR at high temperature is superior to AR. The addition of crumb rubber not only improves the temperature susceptibility, but also enhances its viscoelasticity at low temperatures. After the crumb rubber swell in the asphalt system, the network structures are crosslinked and the physical and chemical effects are produced, such as cracking and repolymerization in the asphalt system. TOR can further enhance the swelling and network crosslinking effects of rubber-asphalt. The TAR has the strongest weather resistance. The study provides guidance for AR and TAR to be used in alpine regions.