Clear mechanistic insights into excited state dynamics in thiolate-protected gold nanoclusters are vital for understanding the origin of the photocatalytic enhancement via metal nanoparticles in the visible region. Extensive experimental studies on the [Au25(SR)18]-1 thiolate-protected gold nanocluster nonradiative relaxation dynamics reported very distinct time constants which span from the femtosecond to nanosecond scale. In this work, the nonradiative excited state relaxations of the [Au25(SH)18]-1 cluster are investigated theoretically to characterize the electron relaxation dynamics. The core and higher excited states lying in the energy range 0.00-2.20 eV are investigated using time-dependent density functional theory (TD-DFT). The quantum dynamics of these states is studied using a surface hopping method with decoherence correction, augmented with a real-time approach to DFT. Population transfer from the S1 state to the ground state occurs on the several hundred picoseconds time scale. Relaxation between excited states that arise from core-to-core transitions is found to occur on a much shorter time scale (2-18 ps). No semiring or other states are observed at an energy lower than the core-based S1 state. This observation suggests that the several picosecond time constants observed by Moran and co-workers could arise from core-to-core transitions rather than from a core-to-semiring transition. A large energy gap between the S7 and S6 states is found to be responsible for a relatively slow decay time for S7. The S1 state population decrease demonstrates the slowest decay time due to the large energy gap to the ground state. The spectral densities are calculated to understand the electron-phonon interactions that lead to electronic relaxations.