Nano titanium oxide memristor is expected to be the basic cell of a new generation of resistive memory and applied in the control and data storage systems of spacecrafts that work in a radiation environment. The changes of radiation key factors, such as energy, intensity, direction, and duration etc. probably have an influence on the radiation damage of the titanium oxide memristor. However, there has been no relatively detailed research of it. Based on the SRIM simulation, with the Monte Carlo method used as its core, the main part of cosmic rays——proton and alpha rays and the relevance between the key factors and radiation damage in titanium oxide memristor are quantitatively studied. According to the experimental data, the relations between key factors and R_{ON}, R_{OFF}, the mobility of oxygen vacancies are analyzed. We find that the mobility of oxygen vacancies increases abruptly when the ratio between oxygen vacancies and titanium oxide molecules is greater than 0.16. Moreover, compared with proton radiation, the alpha particle radiation going into the active region in titanium oxide memristor, especially at an oblique incidence angle may cause a greater damage to the device and should be strictly avoided, and the radiation damage increases as the intensity and duration of the radiation are raised. SPICE simulations are further utilized to show the influence of radiation on the characteristics of the coexistence of dopant drift and the tunnel barrier. We also find that the titanium oxide memristor device will gradually turn into a normal resistor with a low resistance and lose its charge-memory ability after persistent radiations. This work provides support for evaluating and reducing radiation damage for titanium oxide memristors, so as to improve the reliability of the device in radiation environment.