Abstract: The present disclosure relates to the field of Chemical Vapor Deposition (CVD) diamonds and their processing after fabrication. In particular, the present disclosures provides a method for coring and slicing a CVD diamond product, wherein the CVD diamond product comprises a CVD diamond and graphitized material covering several side-faces of the diamond. The method is carried out by an apparatus that provides a laser beam coupled into a fluid jet. The method comprises, for the coring, cutting the product with the laser beam to remove the graphitized material from the side-faces of the diamond. Further, the method comprises, for the slicing, cutting off one or more slices from the diamond with the laser beam.