Etymology
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saw (n.1)

[toothed cutting tool] Middle English saue, from Old English sagu, from Proto-Germanic *sago "a cutting tool" (source also of Old English seax "knife," Old Norse sög, Norwegian sag, Danish sav, Swedish såg, Middle Dutch saghe, Dutch zaag, Old High German saga, German Säge "saw"), from PIE root *sek- "to cut" (source also of Latin secare "to cut").

In reference to its use as a musical instrument, by 1905. Saw-grass, the long, toothed grass found in the Southern U.S., is attested by 1822. The saw-fly (1773), destructive to plants, is so called for the construction of the insect's egg-depositing organ.

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saw (n.2)

[proverb, saying, maxim], Middle English saue, at first in a general sense, "what is said, talk, words," from Old English sagu "saying, discourse, speech, study, tradition, tale," from Proto-Germanic *saga-, *sagon- (source also of Middle Low German, Middle Dutch sage, zage, German Sage "legend, fable, saga, myth, tradition," Old Norse saga "story, tale, saga"), from PIE root *sek(w)- "to say, utter" (see say (v.)).

The surviving specific sense of "proverb, saying, maxim" is by late 13c. "[A] contemptuous term for an expression that is more common than wise" [Century Dictionary].

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saw (v.)

"cut or cut in pieces with a saw," c. 1200, sauen, saghen, from saw (n.1). Strong conjugation (sawn) began by c. 1400 on model of draw, etc. Related: Sawed; sawing. Sawed-off "short, cut short" is attested by 1887, by 1898 specifically of shotguns.

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saw (v.)
past tense of see; from Old English plural sawon.
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buzz-saw (n.)
"circular saw," 1849, American English, from buzz (v.) + saw (n.). So called from the sound it makes when in operation.
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whip-saw (n.)
also whipsaw, 1530s, from whip + saw (n.). As a verb from 1842. Related: Whip-sawed; whip-sawing.
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band-saw (n.)
also bandsaw, "endless band of steel with a serrated edge," 1847, from band (n.1) + saw (n.1). Said to have been invented 1809 by William Newberry of London.
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rip-saw (n.)

"a hand-saw the teeth of which have more rake and less set than a cross-cut saw, used for cutting wood in the direction of the grain" [Century Dictionary], 1846, from rip (n.) "split timber" (see rip (v.) + saw (n.1)).

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pit-saw (n.)

"large saw used for cutting timber, operated by two men, one (the pit-sawyer) standing in the pit below the log that is being sawed, the other (the top-sawyer) standing on the log," 1670s, from pit (n.) + saw (n.1).

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chain-saw (n.)

also chain saw, chainsaw; 1818 as a surgical apparatus (for amputations) consisting of a chain, the links of which have serated edges; 1835 in the saw mill sense, "power-driven saw consisting of a chain with cutting points attached to the links;" from chain (n.) + saw (n.).

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