A portable and transportable die cavity modifying machine having a base carrying a carriage adjustable along one axis, e.g., a generally horizontal axis, and a machining head adjustable along another axis, e.g., a generally vertical axis, for modifying a die cavity of a stamping die in a manner that prevents blank or slug pulling during stamping press operation. The machine includes a stop that is adjustably connected to the carriage. The stop is configured to limit movement of the machining head along the generally vertical axis. The machine may also feature a vibration isolator that is used with the stop to prevent noise and vibration that result from movement of the machining head in relation to the stop. Additionally, the machine may include an optical device capable of capturing an image of the die cavity defining sidewall as the rotary grinding bit machines the elongate slug retention groove.