The diverse mechanical properties of the F-actin cytoskeleton mediate essential physical behaviors of the cells, including cell division, migration, and shape change. These properties include strain stiffening and stress relaxation that limit cell shape change and determine its rate. To date, stress relaxation has been mainly attributed to the transient nature of cross-linkers that connect F-actins. By contrast, the potential impacts of rich F-actin dynamics to the stress relaxation have been neglected in most previous studies. Thus, in this study, we use a novel computational model to demonstrate that F-actin severing arising from compression-induced filament buckling coordinates with cross-linker unbinding, leading to very distinct modes of stress relaxation. Furthermore, we establish the conditions under which the F-actin severing dominates the mechanical response, providing additional mechanistic insight into the viscoelasticity of the F-actin cytoskeleton.