Electrically reconfigurable spin-wave transport is central to realizing energy-efficient magnonic information technologies, yet existing current-driven approaches require current densities that undermine the fundamental dissipation advantage of spin-wave-based signal processing. Here, we demonstrate low-power electrical control of spin-wave propagation in a hybrid magnonic device comprising a low-damping yttrium iron garnet (YIG) film coupled to an adjacent vanadium dioxide (smallVO₂) stripe. Passing a small current through smallVO₂ triggers its insulator-to-metal transition (IMT), producing a sharp, reversible resistivity reduction exceeding three orders of magnitude. This abrupt phase transition locally modifies the spin-wave dispersion in YIG, reducing the group velocity and suppressing transmission by up to 40 dB near the ferromagnetic resonance frequency. Pulsed current excitation enables reconfiguration of spin-wave transport on a 10 ms timescale. Temperature-dependent measurements, corroborated by thermal modeling, decouple the respective contributions of current-induced heating of YIG and the IMT in smallVO₂, establishing the latter as the dominant control mechanism. Our results demonstrate that electrically induced phase transitions in correlated oxides constitute an energy-efficient strategy for dynamic spin-wave manipulation, providing a scalable route toward reconfigurable magnonic devices.