Mush

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late 17th century (in mush1 (sense 3 of the noun)): apparently a variant of mash.

wiktionary

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Probably a variant of mash, or from a dialectal variant of Middle English mos(“mush, pulp, porridge”); compare Middle English appelmos(“applesauce”), from Old English mōs(“food, victuals, porridge, mush”), from Proto-West Germanic *mōs, from Proto-Germanic *mōsą(“porridge, food”), from Proto-Indo-European *meh₂d-(“wet, fat, dripping”). Cognate with Scots moosh(“mush”), Dutch moes(“pulp, mush, porridge”), German Mus(“jam, puree, mush”), Swedish mos(“pulp, mash, mush”). See also moose.

From Old High German muos and Goidelicmus(“a pap”) or muss(“a porridge”), or any thick preparation of fruit.

Believed to be a contraction of mush on, from Michif, in turn a corruption of French marchons! and marche!, the cry of the voyageurs and coureurs de bois to their dogs.

Simple contraction of mushroom.

From Angloromani mush(“man”), from Romani mursh, from Sanskrit मनुष्य(manuṣya, “human being, man”).

Compare French moucheter(“to cut with small cuts”).

etymonline

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mush (n.)

"kind of porridge; meal boiled in water or milk until it forms a thick, soft mass," 1670s, in the American colonies, a variant of mash (n.) "soft mixture." Meaning "anything soft and thick" is attested from 1824.

mush (interj.)

command to sled dogs, 1897, first recorded 1862, as mouche, perhaps altered from French marchons! "advance!" (imperative of marcher "to march;" see march (v.)). Related: Musher.

mush (v.)

"to pound to a pulp," 1781, from mush (n.). Related: Mushed; mushing.