Diamond tools with a ceramic matrix might solve the problem of improving the quality of precision abrasive machining of ceramic materials, glass, minerals. The paper considers diamond-bearing material with a ceramic bond made of Al2O3 oxide, which has high grinding performance without dressing of a cutting surface. The authors analyze the effect of structural and dynamic parameters of diamond-abrasive processing experimentally and theoretically, determine their rational values. They establish that the determining factors are the load on a tool, diamond concentration and grain size, physical and mechanical properties of interacting materials: diamonds, bond and a workpiece. For a diamond abrasive material with a ceramic matrix, the authors confirm the power law dependence of grinding performance and diamond consumption in the abrasive tool worn layer on the pressure on the tool and diamond granularity. The degree index is determined by the type of machining. The specific diamond consumption depends on the grain concentration, as well as physical and mechanical properties of interacting surfaces. The paper evaluates the feed depth in relation to a diamond size, processing speed, and the choice of a diamond grade. It also gives a phenomenological dependence to estimate the part surface roughness. The proposed analytical dependences of grinding performance and specific diamond consumption have good convergence with the experimental results. Tools made of diamond-bearing material with a ceramic bond demonstrated grinding performance 2–5 times higher than tools with traditional bonds.