Yielding of dynamically crosslinked hydrogels, or the transition between a solid-like and liquid-like state, allows facile injection and utility in translational biomedical applications including delivery of therapeutic cells. Unfortunately, the time-varying nature of the transition is not well understood, nor are there design rules for understanding the effects of yielding on encapsulated cells. Here, we unveil underlying molecular mechanisms governing the yielding transition of dynamically crosslinked gels currently being researched for use in cell therapy. We demonstrate through nonlinear rheological characterization that the network dynamics of the dynamic hydrogels dictate the speed and character of their yielding transition. Rheological testing of these materials reveals unexpected elastic strain stiffening during yielding, as well as characterization of the rapidity of the yielding transition. A slower yielding speed explains enhanced protection of directly injected cells from shear forces, highlighting the importance of mechanical characterization of all phases of yield-stress biomaterials.