Cold mixed epoxy asphalt mixture (CMEAM) is widely applied on steel deck bridge pavements due to its excellent high temperature and fatigue resistance. However, previous studies investigated above two properties through destructive test or without considering water-damage factor, respectively, which is far away from real servicing condition. To distinguish above two properties of EA-05 and EA-10 (mixture with nominal maximum particle size of 4.75 mm and 9.5 mm), uniaxial static creep tests, dynamic modulus test and four-point bending beam fatigue test were applied in this paper. At the same time, to comprehensively acquire elastic, viscous-elastic and plastic performance of CMEAM, four kinds of constitutive models were also put forward. Results showed that seven-element viscous-elastic-plastic creep model has the highest correlation coefficients which proves there exists plastic deformation in CMEAM. Meanwhile, EA-10 is likely to present viscous-elastic deformation while EA-05 is more likely to show plastic deformation. Dynamic modulus among different gradation type mixture at 40 °C is not so apparent. But with the increase of frequency and testing temperature, this difference would be clear. The middle gradation of EA-10 has the most excellent high temperature stability under dynamic load. In terms of the resistance to fatigue damage of control or freeze-thaw treated samples, EA-05-U(the upper limit of EA-05 gradation type) always takes the first place and has the lowest sensitivity to the change of stress level and water damage.