We propose the concept, synthesis, analysis, and design of graphene-based plasmonic tunable low-pass filters operating in the terahertz band. The proposed structure is composed of a graphene strip transferred onto a dielectric and a set of polysilicon dc gating pads located beneath it. This structure implements a stepped impedance low-pass filter for the propagating surface plasmons by adequately controlling the guiding properties of each strip section through graphene's field effect. A synthesis procedure is presented to design filters with desired specifications in terms of cutoff frequency, in-band performance, and rejection characteristics. The electromagnetic modeling of the structure is efficiently performed by combining an electrostatic scaling law to compute the guiding features of each strip section with a transmission line and transfer-matrix framework, approach further validated via full-wave simulations. The performance of the proposed filters is evaluated in practical scenarios, taking into account the presence of the gating bias and the influence of graphene's losses. These results, together with the high miniaturization associated with plasmonic propagation, are very promising for the future use and integration of the proposed filters with other graphene and silicon-based elements in innovative terahertz communication systems.