Squash

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mid 16th century (as a verb): alteration of quash.

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From Middle English squachen, squatchen, from Old French esquacher, escachier, from Vulgar Latin *excoāctiāre, from Latin ex + coāctāre. Probably influenced by Middle English quashen, quassen, from Old French esquasser, escasser(“to crush, shatter, destroy, break”), from Vulgar Latin *exquassare, from Latin ex- + quassare(“to shatter”) (see quash).

Shortening of Narragansett askutasquash(“[a vegetable] eaten green (or raw)”), from askut(“green, raw”) +‎ asquash(“eaten”). [2]

Clipping of  musquash. 

etymonline

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squash (v.)

"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.