We present a comprehensive temperature-dependent inelastic light scattering (Raman) study on single crystals of two-dimensional CuCrP₂S₆, a layered van der Waals material exhibiting coupled magnetic and electric degrees of freedom. Raman measurements were performed from 5 to 300 K to probe the phonon dynamics across multiple structural and magnetic phase transitions. Our analysis reveals pronounced thermal hysteresis in phonon frequency, line width, intensity and dynamic Raman susceptibility, confirming the first-order nature of the antipolar transition near T_C1 ∼ 145 K and a second-order transition near T_C2 ∼ 190 K. Low-frequency modes associated with Cu⁺ and Cr³⁺ ions exhibit softening and anomalous line width behavior, in particular phonon mode P2 (∼37 cm^–1), which shows nonmonotonic temperature dependence and intensity enhancement near 60 K, suggesting persistent off-center Cu⁺ dynamics in the quasi-antipolar phase. The coexistence and coupling of soft phonon modes and central peaks indicate a crossover from displacive to order–disorder type transition mechanisms. Additionally, phonon anomalies below the Néel temperature (T_N ∼ 32 K) reflect spin-phonon coupling, linking lattice vibrations to long-range magnetic correlations. Our findings provide critical insight into the lattice instabilities, symmetry evolution, and quasiparticle interactions in CuCrP₂S₆, offering a deeper understanding of phase transition dynamics in two-dimensional multiferroic systems and guiding the future design of magnetoelectric and spintronic devices.