A type of gradient-degraded material-induced trigger has a greater potential to induce a progressive crushing mode in a controlled manner to reduce the initial crushing load and increase the specific energy absorption. Thus, different material degradation strategy-based triggers are designed to improve the crashworthiness of composite tubes. To understand the triggering mechanisms, effects of height of trigger and level of degradation are studied using single material degradation strategies. In turn, gradient material degradation strategies are novelly presented to explore different crushing behaviors of tube. Further, an improved gradient material degradation gathering all features of single material degradation and gradient material degradation is proposed. The virtual quasi-static crushing tests are conducted where the model considers intra-ply and inter-ply failure initiation and damage evolution. The crushing behaviors of all triggered tubes are compared. From the predicted results, it is found that both the height of trigger and level of degradation have significant effects on the crushing behavior. The multi-phased or progressive initial crushing process is presented by using gradient material degradation. By comparison, the tube using the improved gradient material degradation presents 8.26% lower peak load, 8.75% higher specific energy absorption, and 25% higher crushing load stability than the original tube.