The voltage modulation in spin dynamics via the spin-lattice coupling (SLC) effect has been investigated in epitaxial La_0.5Sr_0.5MnO₃/PMN-PT multiferroic heterostructures. The critical angle for the disappearance of the first exchange (FEX) spin wave has been observed around 67° experimentally and been shifted about 4° by applying an electric field (E-field). In particular, at the critical angle, the FEX spin wave can be switched “on” and “off” by voltages, showing great potential in realizing magnonic devices. Moreover, the FEX spin wave resonance shift of 187 Oe at 173 K has been realized by the voltage driven SLC effect, which is a little larger than piezostrain-induced ferromagnetic resonance shift of 169 Oe. The experimental results can be well-explained by the modified Puszkarski spin wave theory.