The mid-infrared (MIR) region is attracting increasing interest for on-chip synchronous detection and free-space optical (FSO) communications. For such applications, a high-performance electro-optical modulator is a crucial component. In this regard, we propose and investigate a graphene-based electro-absorption modulator (EAM) and microring modulator (MRM) using the suspended germanium waveguide platform. The modulators are designed for the second atmospheric window (8 to 12 µm). The incorporation of double-layer graphene on the suspended slot waveguide structure allows for the significant enhancement of light-graphene interaction, theoretically achieving a 3-dB bandwidth as high as 78 GHz. The EAM shows a calculated modulation depth of 0.022-0.045 dB/µm for the whole operation wavelength range. The MRM exhibits a calculated extinction ratio as high as 68.9 dB and a modulation efficiency of 0.59 V·cm around 9 µm. These modulators hold promise for constructing high-speed FSO communication and on-chip spectroscopic detection systems in the MIR atmospheric window.