A method of making a cutting element includes subjecting a mixture of diamond particles and a carbonate material to high-pressure high-temperature sintering conditions to form a sintered carbonate-polycrystalline diamond body having a diamond matrix of diamond grains bonded together and carbonates residing in the interstitial regions between the diamond grains, the carbonate material having a non-uniform distribution throughout the diamond matrix. The carbonate-polycrystalline diamond body is subjected to a controlled temperature, a controlled pressure condition or a combination thereof, to effect an at least partial decomposition of the carbonate material.