"to cut or sever with a sharp instrument," c. 1200, from a Scandinavian source (compare Old Norse klippa, Swedish klippa, Danish klippe "clip, shear, cut"), which is probably echoic. Related: Clipped; clipping.
Meaning "to pronounce words in a shortened form" is from 1520s. The verb has a long association with shady activities, originally especially in reference to cutting or shaving metal from coins (c. 1400), but later extended to swindles from the sense "to shear sheep," hence clip-joint "place that overcharges outrageously" (1933, American English, a term from Prohibition).
To clip (someone's) wings, figuratively, "put a check on one's ambition" (1590s) is from the method of preventing a captive bird from flying.
"fasten, hold together by pressure," also (mostly archaic) "to embrace," from Old English clyppan "to embrace, clasp; surround; prize, honor, cherish," from Proto-Germanic *kluppjan (source also of Old Frisian kleppa "to embrace, love," Old High German klaftra, German klafter "fathom" (on notion of outstretched arms). Also compare Lithuanian glėbys "armful," globti "to embrace."
Meaning "to fasten, bind" is early 14c. Meaning "to fasten with clips" is from 1902. Related: Clipped. Original sense of the verb is preserved in U.S. football penalty (see clipping (n.1)).