My guess is the dust created is similar to grinding dust from masonry/concrete/plaster cutting. I have a dedicated vac vor that kind of work (also use it for drywal sanding.
The dust created is fine, but heavy, and if you use a regular vac, it will clog the pores of the bag and suction will decrease quickly. (way before the bag is even 1/3rd full)
The vac I use has automatic filtercleaning, It's used without a bag, and when you turn of the tool connected if it has run for at least 2minutes, it wil automatically shake the filters, and the dust falls off, and the power of the suction remains.
If I use that vac to collect other dust (wooddust/ shavings / house dust, that dust will clog up the folds of the filter, and the electromagnetic cleaning won't work anymore... I'm going to get dustbags for that vac aswell, so I can use it for more purposes (and take the bag back out for grinding).
I can cut walls nearly dustfree, the first pass gives no dust, the second one will leak some dust through the already existing groove of the first cut; cutting grooves for electric pipes is dustfree, because they can be done in 1 pass. But usually when I have to cut through a wall I use watercooling, if possible (ground floor, no wooden floor)