In the correlated kagome metal CsCr${}_3$Sb${}_5$, the interplay among lattice, charge, and spin degrees of freedom governs its rich quantum phases, yet remains poorly understood. Here, we present a comprehensive investigation of these couplings through temperature- and magnetic field-dependent polarized Raman spectroscopy. Our polarization-resolved measurements unambiguously identify a structural phase transition at $T^{*}\approx 55K$, establishing a low-temperature (LT) orthorhombic phase. A striking reduction in phonon linewidths below $T^{*}$ reveals the suppression of electron-phonon coupling (EPC) coinciding with the opening of a charge density wave gap. Remarkably, upon suppression of EPC, a robust spin-phonon coupling (SPC) emerges in the magnetically ordered state, as evidenced by anomalous phonon broadening and pronounced magnetic field modulation of phonon intensities. These findings not only clarify the low-temperature structure of CsCr${}_3$Sb${}_5$ but also establish a clear boundary between the EPC-dominated and SPC-active phases, offering key spectroscopic evidence for understanding the unconventional physics in this strongly correlated kagome metal.