The polarization-resolved nonlinear dynamics of vertical-cavity surface-emitting lasers (VCSELs) subject to orthogonally polarized optical pulse injection are investigated numerically based on the spin flip model. By extensive numerical bifurcation analysis, the responses dynamics of photonic neuron based on VCSELs under the arrival of external stimuli of orthogonally polarized optical pulse injection are mainly discussed. It is found that, several neuron-like dynamics, such as phasic spiking of a single abrupt large amplitude pulse followed with or without subthreshold oscillation, and tonic spiking with multiple periodic pulses, are successfully reproduced in the numerical model of VCSELs. Besides, the effects of stimuli strength, pump current, frequency detuning, as well as the linewidth enhancement factor on the neuron-like response dynamics are examined carefully. The operating parameters ranges corresponding to different neuron-like dynamics are further identified. Thus, the numerical model and simulation results are very useful and interesting for the ultrafast brain-inspired neuromorphic photonics systems based on VCSELs.