1825, "electrotype, stereotype," from French cliché, a technical word in printer's jargon for "stereotype block," noun use of past participle of clicher "to click" (18c.), supposedly echoic of the sound of a mold striking metal (compare native click).
Originally, a cast obtained by letting a matrix fall face downward upon a surface of molten metal on the point of cooling, called in English type-foundries 'dabbing.' [OED]
Figurative extension to "trite phrase, worn-out expression" is first attested 1888, via the notion of the metal plate from which a print or design could be reproduced endlessly without variety, paralleling the sense evolution of stereotype. But this sense was not common in English until the 1920s, when it was identified as a French idiom. Related: Cliched (1928).