A cutting tool stop-control apparatus according to the invention is for controlling the stopping of a cutting tool when executing a hole drilling operation by a machining center or milling machine, and particularly when executing a back-boring operation. When the tool is subjected to an emergency return, depending on the actual conditions which prevail when an operation is suspended, the tool is withdrawn to the cycle starting point along an optimum path in accordance with a continuance program, and the prescribed operation is resumed automatically after the tool is changed.