The precise tuning of local spin states in adsorbed organometallic molecules by a mechanically controlled scanning tunneling microscope (STM) tip has become a focus of recent experiments. However, the underlying mechanisms remain somewhat unclear. We investigate theoretically the STM tip control of local spin states in a single iron(II) porphyrin molecule adsorbed on the Pb(111) substrate. A combined density functional theory and hierarchical equations of motion approach is employed to simulate the tip tuning process in conjunction with the complete active space self-consistent field method for accurate computation of magnetic anisotropy. Our first-principles-based simulation accurately reproduces the tuning of magnetic anisotropy realized in experiment. Moreover, we elucidate the evolution of geometric and electronic structures of the composite junction and disclose the delicate competition between the Kondo resonance and local spin excitation. The understanding and insight provided by the first-principles-based simulation may help to realize more fascinating quantum state manipulations.