The improved split Hopkinson pressure bar (SHPB) was used to study the dynamic mechanical properties and failure characteristics of surrounding rock in deep rock mass engineering that is under high stress and affected by blasting excavation and other dynamic disturbances. In a three-dimensional high static load and frequent dynamic disturbance test, the preload high axial pressure and confining pressure are used to simulate the high crustal stress of deep rock, and the effect of small disturbances on the rock is simulated by the low impact load. The results show that there are two types of dynamic stress-strain curves of deep rock: an elastic-plastic curve and plastic-elastic-plastic curve. The curves consists of five parts: the compaction stage, micro-crack steady development stage, micro-crack unstable propagation stage, fatigue damage stage, and fatigue failure stage. Reductive phenomena of constringent strain after dynamic peak stress appear because of the different degrees of rock damage. Moreover, these phenomena include two conditions, namely, whether rebound occurs or not. The impact resistance of rock is strongest when the ratio of the confining pressure to axial pressure is optimal, and the dynamic average strength of rock and accumulative impact times decrease with the increase of the preloaded axial compression and increase with the increase of the preloaded confining pressure. Both the dynamic deformation modulus and dynamic peak stress decrease with the increase of the accumulative impact time, while the maximum strain and the dynamic peak strain increase. The corresponding rebound strain as a whole first increases and then decreases with the increasing impact times. For deep rock, tensile failure and single-bevel plane shear failure are the main failure modes, and pull-compression mixed friction failure is the auxiliary failure mode. Additionally, the lumpiness of broken rock decreases with the increase of the preloaded axial compression and increases with the increase of the preloaded confining pressure.