The possibility of alloying the powder alloy of the Fe-Cu-Co-Sn system with multilayered carbon nanotubes (MCNTs) in order to form a dispersion-hardened composite material with improved mechanical and tribological properties, which can be used as a binder for a diamond cutting tool, is considered. The mixing mode of carbon nanotubes with the starting powder binder is selected. The dependence of physicochemical properties of the composite material on the MCNT content is investigated in a range of 0.01–3%. The composite binders with the optimal MCNT content at a level of 0.01% are fabricated. The alloy is characterized by improved mechanical properties; namely, hardness increases by 9–11 HRB units and the bending strength for three-point bending increases by 100 MPa.