The present work focuses on the effect of vanadium dioxide (VO2) films exhibiting a metal-insulator transition (MIT) on performance characteristics of the magnetic multilayers. It has been shown that the MIT provides a novel mechanism for controlling the microwave spin-wave dynamics in the yttrium-iron garnet (YIG) films. In particular, the low and high levels of microwave attenuation of spin waves transmitted through the YIG-VO2 bilayer has been observed due to a variation of the VO2 conductivity within a narrow temperature range. This effect has been utilized to realize fully reconfigurable magnonic crystals composed of the thickness-modulated YIG and regular VO2 films. Promising functionality of the proposed waveguiding structures arises from a controllability of wave intensity, which provides altering of the frequency response from an original band structure to a full rejection of spin waves.Numerical simulations taking into account both the YIG-film saturation magnetization and the VO2-film conductivity have confirmed the experimentally observed spin-wave dynamics. An interest in ferrite-VO2 bilayers arises not only from possible practical applications, but also from a variety of fundamental scientific problems devoted to physics of wave phenomena in planar thin-film magnetic multilayers.