Based on triply periodic minimal surfaces structures, the Gyroid type mechanical metamaterials are proposed, and the quasi-static and dynamic properties of the proposed structure are investigated. Firstly, the quasi-static compression tests of the Gyroid structure with the relative density of 30%, 40% and 50% are performed to investigate the effect of the density on quasi-static mechanical properties. Results found that, the structure modulus and average plateau stress increase exponentially with the increase of equivalent density, and Gibson-Ashby model is used to predict the change rules. Then, the influence of dynamic loadings on mechanical response of minimal surfaces mechanical metamaterials is investigated. According to the influence factors and variation tendence, the rigid-perfectly plastic-lock model and simplified prediction model of energy absorption are conducted to predict the crushing strength and energy absorption of gyroid structures under dynamic impact. This work demonstrated that, the mechanical metamaterials based on triply periodic minimal surface structure possess prominent load bearing and impact resistance capability, and the key performance can be predicted by the theoretical model, which provide theoretical foundation of the design of highperformance protective structure.