A sewing machine has at least one sewing head having a presser foot which is vertically reciprocally moved by a predetermined stroke in synchronism with a vertical movement of a needle bar. After completion of the sewing operation, an upper thread is cut in a position spaced by a suitable distance from a sewing needle mounted on the needle bar. A refuge mechanism is operable to move the presser foot to a refuge position for giving refuge to a part of the upper thread on the side of the sewing needle cut after completion of the sewing operation. The refuge position is out of the predetermined stroke.