A method of forming a composite cutter for a downhole drilling tool is described. The method includes: mixing a polycrystalline diamond powder and a cubic boron nitride powder with a molar ratio between 0.1 and 0.9 to form a catalyst-free composite mixture; placing the catalyst-free composite mixture into a mold configured in a shape of a cutter; exposing the catalyst-free composite mixture to an ultra-high-pressure, high-temperature treatment including a pressure between 11 Gigapascals (GPa) and 20 GPa, and a temperature between 1300 Kelvins (K) and 2600 K to form a solid composite body; and cooling the solid composite body to form the composite cutter.