mid-14c., "condiment for meat, fish, etc.; pickling liquid, brine," from Old French sauce, sausse, from Latin salsa "things salted, salt food," noun use of fem. singular or neuter plural of adjective salsus "salted," from past participle of Old Latin sallere "to salt," from sal (genitive salis) "salt" (from PIE root *sal- "salt").
From late 14c. as "a curative preparation, medicinal salt." Often in 15c.-17. sawce, salse; constant reimportation of the word in French cookery terms might have helped keep the older spelling. Also formerly applied broadly in provincial English and U.S. to condiments of any kind, especially garden vegetables or roots eaten with meat (1620s), also known as garden-sauce.
Figurative meaning "something which adds piquancy to words or actions" is recorded from c. 1500; the sense of "impertinence" is by 1835, but the connection of ideas in it is much older (see saucy, and compare sass). Slang meaning "liquor" is attested by 1940. Figurative phrases suggesting "subject to the same kind of usage" is by 1520s (serued with the same sauce).