"to crush, squeeze," early 14c., squachen, from Old French esquasser, escasser "to crush, shatter, destroy, break," from Vulgar Latin *exquassare, from Latin ex- "out" (see ex-) + quassare "to shatter" (see quash "to crush"). Related: Squashed; squashing.
squash (n.1)
gourd fruit, 1640s, shortened borrowing from Narraganset (Algonquian) askutasquash, literally "the things that may be eaten raw," from askut "green, raw, uncooked" + asquash "eaten," in which the -ash is a plural affix (compare succotash).
squash (n.2)
1610s, "act of squashing," from squash (v.). The racket game called by that name 1899; earlier (1886) it was the name of the soft rubber ball used in it.