The invention provides a shape member manufacturing apparatus and a shape member manufacturing method which aims at cutting and grinding a joint projection 8B formed when a plurality of shape members are joined together by welding or friction stir welding, in a short time with high accuracy. A plurality of mounts 11 having a side structure 8 placed thereon are arranged in the longitudinal direction of the side structure. A joint projection 8B of a welded portion or a friction stir welded joint is formed on the surface of the side structure 8 in its longitudinal direction. A carrier 100 travels in the longitudinal direction of the side structure 8. Columns 105 are installed in a girder 103 of the carrier, and a milling cutter device 80 and a grinding device 90 are installed in lower portions of the columns 105. A milling surface of a milling cutter 81 of the milling cutter device 80 has a circular-arc shape with a radius R. The milling cutter 81 performs cutting at an angle θ1 tilted with respect to a vertical line. Further, the milling cutter device is provided with sliding plates 85. The milling cutter device performs cutting with the sliding plates 85 brought into contact with the surfaces of the extruded shape members.