A metal–organic framework (MOF) material Mg-MOF-74 was prepared by a solvothermal method, and the influence of the solvent volume and mass–liquid ratio on the preparation process was investigated. Based on the iron-based modified biochar FeCeCu/BC obtained by the sol–gel method, functionalized modified MOF-based biochar composites were prepared by the physical mixing method, co-pyrolysis method, sol–gel method and in situ growth method. The mercury removal performance and structural characteristics of the samples were studied, and the adsorption mechanism and key action mechanism were studied by using the adsorption kinetic model. Increasing the solvent volume and the mass liquid ratio will make the crystallization and pore structure of Mg-MOF-74 worse and its mercury removal performance poor. For MOF-based FeCeCu/BC composites, the mercury removal performance of the composite samples prepared by the sol–gel method and co-pyrolysis method is the best, at 31% and 46% higher than that of modified biochar, respectively. Mg-MOF-74 plays a role in promoting pyrolysis and changing the pore structure in the composite. The mercury removal process of composite materials is the result of physical adsorption and chemical adsorption, external mass transfer and internal diffusion.