A method or process for making polycrystalline diamond or polycrystalline CBN cutting tools (Superabrasives) (501), which have integral chip-breaking features (504) is disclosed. This method involves pressing a die or other rigid component against either an outer can cover or the diamond or CBN region directly. This invention provides economical manufacture of diamond chip-breaker tools (501), while avoiding unnecessary EDM EDG, grinding or laser processes. This process forms the chip-breaker (504) on the upper surface of the diamond region (503), during or prior to sintering. This invention permits a wide variety of chip-breaker (504) or other diamond surface features, while minimizing cost and processing steps. Disclosed embodiments include: pressing through the can assembly; pressing within the assembly by introducing a rigid component in the can; and pressing two cans together with an intervening rigid component imposing the desired diamond surface features.