We report a preliminary computational study of the rate-dependent behavior of a polycrystal magnesium alloy under varying levels of stress triaxiality conditions. Smooth and notched round bar specimens with a strong initial texture are considered to achieve different levels of stress triaxiality. Full three-dimensional crystal plasticity simulations are conducted, which mimic tensile Kolsky bar experiments. The results indicate that the material rate sensitivity couples with the stress state to produce qualitatively different macroscopic responses that are governed by the interacting microscale deformation mechanisms. While the smooth specimens show macroscopic strain localization resulting in stress softening immediately following the initial yield, notched bars exhibit increasingly stable responses with increasing notch acuity. Deformation anisotropy is tempered with increasing stress triaxiality and strain rate. A micromechanical analysis of the deformation activities is presented to explain the macroscale responses. Stress triaxiality distributions in the notch regions provide insights into probable damage mechanisms as a function of the imposed strain rate.