At high strain rates, the dynamic response of cement mortar, a heterogeneous material with damage, was experimentally studied under three different stress states: (1) one-dimensional stress state by using the SHPB technique, (2) one-dimensional strain state at high pressures from 1 to 5 GPa by using a one-stage gas gun, and (3) quasi one-dimensional strain state by using an improved passive confining SHPB technique. The experimental results indicate that cement mortar is a kind of nonlinear rate-dependent material with internal damage evolution, and that the confining pressure greatly influences its ductility and strength. The main results are given and discussed.