A gap-cutter tool assembly (10) for machining a longitudinal gap in an installed boiler tube (12) is provided with clamp elements (88) that engage the interior surface of the installed boiler tube (12), a cutter head track (26) that provides a straight line cutting path within the tube interior and in the presence of different tube interior diameters, and a cutter head (28) that cooperates with the cutter head track (26) and that has different elevational positions during the cutter head cutting and return strokes, and at the end of the cutter head return stroke.