A method for manufacturing a thread-forming screw having a shank and a thread formed in one piece with the shank and region-wise circumferentially arranged on the shank, is disclosed. After the formation of the thread on the shank, a plurality of recesses is subsequently stamped into the thread. Then, a plurality of compact cutting elements is welded into the recesses in the thread, where the cutting elements are made of a hard material and have a hardness greater than the hardness of the thread. Additionally, a stamping device for carrying out the method is also disclosed.