Spin-crossover combined with metal-insulator transition and superconductivity has been found in 2D transition-metal phosphorous trichalcogenides when tuning them by high pressure. Simulation of such intriguing spin-crossover behaviors is crucial to understanding the mechanism. The Hubbard U correction is widely used to describe the strong on-site Coulomb interaction in the d electrons of transition-metal compounds, while the U values are sensitive to the crystal field and spin state varying greatly with pressure. In this work, we show that taking MnPS3 as an example and based on a uniform parameter set, the hybrid functional calculations give a spin-crossover pressure of 35 GPa consistent with experimental observation (30 GPa), which is less than half of the existing reported value (63 GPa) using the Hubbard U correction. Notably, we find a spin-crossover induced transition from an antiferromagnetic semiconductor with monoclinic stacking-order to a ferromagnetic semiconductor with rhombohedral stacking-order, and the ferromagnetism originates from the partially occupied t2g orbitals. Different from previous understanding, the Mott metal-insulator transition of MnPS3 does not occur simultaneously with the spin-crossover but in a pressurized low-spin phase.