The possibility of directional modification of the operation properties of epoxy composites by using small additions of finely dispersed electrochemically oxidized graphite was demonstrated. The optimum content of oxidized graphite as a structuring additive is 0.1 wt % relative to the epoxy compound. It ensures an 18% increase in the bending stress, a 31% increase in the bending elastic modulus, a 31% increase in the compression strength, a 53% increase in the tensile strength, a 15% increase in the tensile elastic modulus, and a 56% increase in the impact strength. Introduction of oxidized graphite influences the sample self-heating in the course of curing, Namely, the time before the onset of self-heating increases from 104 to 146 min, and the time in which the maximal self-heating temperature is reached, from 146 to 192–195 min, with the maximal self-heating temperature remaining virtually unchanged. Introduction of oxidized graphite increases the heat resistance, softening point, and thermal conductivity coefficient of the epoxy composite.