A method for removing a weld crown from a weld joint between first and second work pieces includes steps of positioning a rotary milling tool proximate to the joint and at an offset angle to set a cutting arc relative to the joint. The milling tool is positioned so the cutting arc intersects the weld crown, weld toes, and parent metal on each side of the weld joint. As the milling tool traverses the joint to cut away the weld crown, the milling tool may tilt from side to side to compensate for misalignment between the work pieces along the weld joint. An apparatus for weld crown removal holds a milling tool at an offset angle, and provides a tracking mechanism to permit the milling tool to track misalignment between the work pieces, maintaining the cutting arc in intersection with the weld toes and parent metal along the weld joint.