1560s, "fix securely (a driven nail) by bending and beating it back," a variant of clench (q.v.). The sense of "settle decisively" is first recorded 1716, from the notion of "clinching" the point of a nail to keep it fast. Boxing sense is from 1860. Related: Clinched; clinching.
1620s, "method of fastening ropes," nautical, from clinch (v.). Also compare clench (n.). Meaning "a fastening by bending a driven nail" is from 1650s. In pugilism, "grappling at close quarters," from 1875.