Two-dimensional (2D) multiferroics offer an appealing platform for electrically and magnetically reconfigurable nonlinear photoresponses. In particular, the bulk photovoltaic (BPV) effect, as a second-order nonlinear optical response rooted in Bloch wave quantum geometry, is highly sensitive to crystalline and magnetic symmetries. Therefore, the BPV effect could serve as a sensitive method to capture subtle symmetries in multiferroic systems with fruitful ferroic order switching. Here, taking a monolayer multiferroic CuCrP2S6 as a representative example, we systematically investigate the BPV effect across the paraelectric (PE)-ferroelectric (FE)-antiferroelectric (AFE) phase transition by combining first-principles calculations with magnetic group symmetry analysis. We explore the influence of phase transition, polarization reversal, multiferroicity, magnetic order, magnetocrystalline anisotropy, and its emergent altermagnetism on the BPV responses. Our results suggest that the BPV effect can effectively distinguish distinct polarization and magnetic states, establishing monolayer CuCrP2S6 as a promising 2D multiferroic platform for electrically and magnetically reconfigurable BPV and nonlinear optoelectronic devices.