Honeycomb extrusion die apparatus include a die body including a first set of die pins circumscribed by a second set of die pins. At least a portion of the end face of die pins of the second set of die pins are positioned along a peripheral surface extending at an oblique angle with respect to the extrusion direction. A lateral width of the open end of a plurality of discharge slots defined by the second set of die pins is larger than a lateral width of the open end of a plurality of discharge slots defined by the first set of die pins. Methods of making a honeycomb extrusion die apparatus are also provided.