We study translocation of semiflexible polymers driven by force fd inside a nanometer-scale pore using our three-dimensional Langevin dynamics model. We show that the translocation time τ increases with increasing bending rigidity κ. Similarly, the exponent β for the scaling of τ with polymer length N,τ∼Nβ, increases with increasing κ as well as with increasing fd. By comparing waiting times between semiflexible and fully flexible polymers we show that for realistic fd translocation dynamics is to a large extent, but not completely, determined by the polymer's elastic length measured in number of Kuhn segments NKuhn. Unlike in driven translocation of flexible polymers, friction related to the polymer segment on the trans side has a considerable effect on the resulting dynamics. This friction is intermittently reduced by buckling of the polymer segment in the vicinity of the pore opening on the trans side. We show that in the experimentally relevant regime where viscosity is higher than in computer simulation models, the probability for this buckling increases with increasing fd, giving rise to a larger contribution to the trans side friction at small fd. Similarly to flexible polymers, we find significant center-of-mass diffusion of the cis side polymer segment which speeds up translocation. This effect is larger for smaller fd. However, this speedup is smaller than the slowing down due to the trans side friction. At large enough NKuhn, the roles can be seen to be reversed, and the dynamics of flexible polymers can be reached. However, for example, polymers used in translocation experiments of DNA are elastically so short that the finite-length dynamics outlined here applies.