"cutting tool," Old English sagu, from Proto-Germanic *sago "a cutting tool" (cf. Old English seax "knife," Old Norse sõg, Norwegian sag, Danish sav, Middle Dutch saghe, Dutch zaag, Old High German saga, German Säge "saw"), from PIE root *sak-/*sek- "to cut" (cf. Latin secare "to cut," Russian sech' "to cut;" see section).
"proverb," Old English sagu "saying, discourse, speech," from Proto-Germanic *saga-, *sagon- (cf. Middle Low German, Middle Dutch sage, zage, German sage "legend, fable, saga, myth, tradition," Old Norse saga "story, tale, saga") from the root of Old English secgan "say" (see say).
early 13c., from saw (n.1). Strong conjugation began 15c. on model of draw, etc. Sawed-off "short, cut short" is attested 1887 of persons, 1898 of shotguns.