In this article, a novel class of dynamically tunable filtering attenuators with high selectivity and continuously tunable attenuation is proposed through the comprehensive design of graphene sandwiched structure (GSS), microstrip line, and half-mode substrate integrated waveguide (HMSIW). The GSSs are loaded on microstrip resonators to reduce the resonance intensity, which results in a valid attenuation in the passband. A co-design method of GSS, microstrip resonator, and HMSIW coupling structure based on the equivalent circuit model is proposed to minimize the impact of graphene on the selectivity of filtering attenuator. A transmission zero located on the upper band is also introduced to enhance the selectivity. By varying the bias voltage on GSSs, a controllable attenuation from 1.7 to 8.4 dB can be obtained over the operating bandwidth centering at 1.72 GHz while preserving good selectivity. It is worth mentioning that the out-of-band suppression of the proposed filtering attenuator is also reduced from 40 to 50 dB. Another tunable filtering attenuator based on microstrip short-ended resonators is also designed to verify the method. Finally, a prototype is fabricated and measured and the measured results are in good agreement with the simulation results.