While the dynamics of a fully flexible polymer ejecting a capsid through a nanopore has been extensively studied, the ejection dynamics of semiflexible polymers has not been properly characterized. Here we report results from simulations of ejection dynamics of semiflexible polymers ejecting from spherical capsids. Ejections start from strongly confined polymer conformations of constant initial monomer density. We find that, unlike for fully flexible polymers, for semiflexible polymers the force measured at the pore does not show a direct relation to the instantaneous ejection velocity. The cumulative waiting time t(s), that is, the time at which a monomer s exits the capsid the last time, shows a clear change when increasing the polymer rigidity κ. The major part of an ejecting polymer is driven out of the capsid by internal pressure. At the final stage the polymer escapes the capsid by diffusion. For the driven part there is a crossover from essentially exponential growth of t with s of the fully flexible polymers to a scale-invariant form. In addition, a clear dependence of t on polymer length N0 was found. These findings combined give the dependence t(s) N00.55s1.33 for the strongly rigid polymers. This crossover in dynamics where κ acts as a control parameter is reminiscent of a phase transition. This analogy is further enhanced by our finding a perfect data collapse of t for polymers of different N0 and any constant κ.