To address the suppression needs of low-frequency broadband flexural waves, metamaterial beams with sandwich-damped resonators based on the constrained layer damping (CLD) mechanism is proposed. First, comparative finite element analysis of “Aluminum-Rubber-Aluminum” and “Rubber-Aluminum-Aluminum” configurations reveals the synergistic "bandgap-dissipation" mechanism behind the superior vibration reduction of the CLD configuration. To overcome the inherent "low-frequency vs. broadband" design trade-off in uniform structures, a gradient design strategy is proposed. Simulation results indicate that the gradient metamaterial beam achieves significant vibration suppression in the 600–2650 Hz frequency range, with a relative bandwidth of up to 126.2%. Finally, experiments validated both uniform and gradient configurations, showing good agreement with simulation trends, notably, a gradient CLD specimen utilizing a Blu-Tack core successfully pushes the attenuation onset frequency down from 1480 Hz (uniform) to 344 Hz and achieves vibration suppression within the ultra-wide 1256–5000 Hz band.