This process for manufacturing a closed loop of cutting wire comprises manufacturing a cutting wire comprising a central core extending continuously between two free ends. The central core having a tensile strength higher than 1400 MPa. The process includes welding the two free ends together to form the closed loop of cutting wire, in which: the manufacture of the cutting wire comprises making the central core from a material that is solid-state weldable. The welding is a solid-state welding operation comprising crushing, at a temperature below the melting point of the material of the central core, one of the free ends against the other of its free ends until the two ends have interpenetrated and formed a single uniform body of material.