Several ways
- Make a quarzite-only stockpile around (or just under) your workshop. Easiest, but not 100% safe : The mason will still take stones from elsewhere, although after a time he'll take from the pile, so order several floodgates to be sure
You can reinforce this with Burrows. In the past I've set up multiple masonic workshops, each surrounded by stockpiles of a different type of stone and then had multiple stone-named burrows enclosing just these areas (plus food/drink/sleep areas), and before burrows I used to do similar restriction with closed and locked doors (obviously with dedicated food/drink/sleeping areas within that sealed-off area, although for short periods it was never so important, as long as you didn't forget, and actually improved the initial speed of production as long as they didn't prefer to do nothing or sleep on the floor rather than keep working during the time that they were unable to deal with their initial need to feed/drink/sleep).
- Forbid every non-quarzite stone with the z-menu. This way, only quartzite will be used for construction and workshops. Problem : it will forbid the workshops designed with a non-quartzite stone (but not blocks), and you'll have to unforbid everything afterward (or you'll have problems with unmovable stones where you want to build something)
Done this too, and specifically unforbidden stones in structures either from the T-menu of the building or via recognising the "in use as a construction" colour from the Z-Stocks menu. When I've been wanting certain numbers of beds of a certain specific woods, recently, I also waited until the last bed was being made of the old stock, marked the one under the T-Menu ({TSK}ed as To Dump so that when I went and unforbid the next set of logs (for the next half dozen beds) and forbid the just-finishing-with wood-type, I could ensure that the precise log that had been marked as Dump could just be unmarked Dump whereas its fellows in the list that are of that log-type were properly Forbidden to prevent over-expending in this task. Micromanagement at its finickiest, I'll admit.
- Use the economic stones z-list, and allow only quartzite to be used in workshops (green on the list). Problem : allowing the other stones afterward is a pain
Of all the methods, this is the one I've used the least, surprisingly. For some reason, it always seemed to be too much hard work.