We present perturbative analytical results of the Landau level quasienergy spectrum, autocorrelation function, and out-of-plane pseudospin polarization for a single graphene sheet subject to intense circularly polarized Terahertz radiation. For the quasienergy spectrum, we find a striking nontrivial level-dependent dynamically induced gap structure. This photoinduced modulation of the energy band structure gives rise to shifts of the revival times in the autocorrelation function and it also leads to modulation of the oscillations in the dynamical evolution of the out-of-plane pseudospin polarization, which measures the angular momentum transfer between light and graphene electrons. For a coherent state, chosen as an initial pseudospin configuration, the dynamics induces additional quantum revivals of the wave function that manifest as shifts of the maxima and minima of the autocorrelation function, with additional partial revivals and beating patterns. These additional maxima and beating patterns stem from the effective dynamical coupling of the static eigenstates. We discuss the possible experimental detection schemes of our theoretical results and their relevance in new practical implementation of radiation fields in graphene physics.