sawtooth (n.)

[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.

Middle English toth "human or animal tooth," from Old English toð (plural teð), from Proto-Germanic *tanthu- (source also of Old Saxon, Danish, Swedish, Dutch tand, Old Norse tönn, Old Frisian toth, Old High German zand, German Zahn, Gothic tunþus), from PIE root *dent- "tooth."

Plural teeth is an instance of i-mutation. The loss of -n- before spirants is regular in Old English, Old Frisian, and Old Saxon: compare goose (n.), five, mouth (n.). Also thought, from stem of think; couth from the stem of can (v.1); us from *uns.

As "appetite, bodily desire" from late 14c. (as in colt's tooth, sweet tooth, dry tooth "thirst," toothsome, and compare figurative use of palate). Application to tooth-like parts (of saws, combs, etc.) is from late 14c.

Tooth and nail "with biting and scratching, with nails and teeth," hence "viciously, furiously" is from early 14c. (as nayles and teþ). To be armed to the teeth is from c. 1300. The tooth-fairy is attested from 1964.