Is it not moving off the floor or are you just moving it around? I had a combination of dirt and drywall dust and the best way I found was a squeegee. I would dump a little soapy water on the floor, mop and then squeegee the water and the dust to the other end. Then shopvac it up water and dirt all together. Try a test spot and see.

Kevin, we had the same problem for quite awhile. Could never get all the dust removed no m,atter what we did. Finally we put down some large carpet tiles and carpet remnants that DH brought home from a job. This worked fine until we finally had carpet installed.

A carpet shampooer would pick up small particles.

Neighbor and I are finishing our basement.

The following works!

After drywall clean it up as good as possible.

Then shop vac the floor.

Then get a mop and a bucket and mop the floor with pine sol.

Then mop it again.

The change your furnance filter.

Dust all gone.