A method of cutting out a part from a workpiece with making partially welded spots in wire electrical discharge machining to keep the part against falling apart away from the workpiece. There is no need to cut anew the welded spot left as in the conventional process. The cut-out parts are cut off at a time after breakage of the welded spots caused by an external impact. The electric processing condition applied across an inter-electrode space between the wire electrode and the workpiece is changed from a cutting phase to a welding phase in which the wire electrode is fused partially at some spots along a cutting path of a predetermined contour on the workpiece to weld together the cut-out part and the workpiece at the fused spot on the wire electrode.