"small particles produced by the work of a saw on wood," 1520s, from saw (n.1) + dust (n.).
Entries linking to sawdust
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.
dust n.
"fine, dry particles of earth or other matter so light that they can be raised and carried by the wind," Old English dust, from Proto-Germanic *dunstaz (source also of Old High German tunst "storm, breath," German Dunst "mist, vapor," Danish dyst "milldust," Dutch duist), from PIE *dheu- (1) "dust, smoke, vapor" (source also of Sanskrit dhu- "shake," Latin fumus "smoke").
Meaning "elementary substance of the human body, that to which living matter decays" was in Old English, hence, figuratively, "mortal life." Sense of "a collection of powdered matter in the air" is from 1570s. Dust-cover "protective covering to keep dust off" is by 1852; dust-jacket "detachable paper cover of a book" is from 1927.
To kick up the (or a) dust "cause an uproar" is from 1753, but the figurative use of dust in reference to "confusion, disturbance" is from 1560s, and compare Middle English make powder fly "cause a disturbance or uproar" (mid-15c.). For bite the dust see bite (v.).