"to cut or sever with a sharp instrument," c.1200, from a Scandinavian source (cf. Old Norse klippa, Swedish klippa, Danish klippe "clip, shear, cut") probably echoic. Related: Clipped; clipping.
Meaning "to pronounce short" 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 (1590s) is from the method of preventing a captive bird from flying.