  We study the $S>1/2$ antiferromagnetic Heisenberg model on the 1/5-depleted
square lattice as a function of the ratio of the intra-plaquette coupling to
the inter-plaquette coupling. Using stochastic series expansion quantum Monte
Carlo simulations, we numerically identify three quantum phases, including the
dimer phase, N\'eel phase and plaquette valence bond solid phase. We also
obtain the accurate quantum critical points that belong to the O(3)
universality class using the large-scale finite-size scaling. Most importantly,
we study the dynamic spin structure factors of different phases, which can be
measured by inelastic neutron scattering experiments. The low-energy
excitations can be explained as triplons in the dimer phase and plaquette
valence bond solid phase. While in the N\'eel phase, the more prominent magnon
mode can be found as the spin magnitude increases. Furthermore, we find a
broader continuum at smaller $S$, which may be the dynamical signature of
nearly deconfined spinon excitations.
