A center cutting or plunging end mill or ball nose end mill has one or more spiral grooves and flutes in the walls of a mill body of cemented tungsten carbide. Each groove includes polycrystalline diamond or cubic boron nitride formed in situ along a leading edge of each flute. Such a groove extends across the cutting end of the mill so that the mill can be used for center cutting or plunging. The vein of diamond-like material may extend to the center of the mill body or may extend almost all of the way to the center, leaving an area of tungsten carbide exposed at the center of the mill body. A high temperature-high pressure press is used for forming the polycrystalline diamond-like veins in situ within the grooves in the mill.