You can clean slate floors regularly with a dust mop a broom and a damp mop.
Chinese slate floor tiles cleaning.
Dry the tiles with a dry mop or cloth.
Use the wet vac to remove the clean water.
In this case the tiles were chinese slate and were proving very difficult for the property owner to keep clean due to the lack of sealer to protect against dirt and stains.
Cleaning and sealing black chinese slate tiles in basingstoke you can see from the photograph below how dirty these black chinese slate tiles and grout had become.
Ideally you should dust mop your slate floor every day and damp mop it once a week.
Riven green slate kitchen floor cleaned and sealed in oldham january 21 2020 dealing with limescale staining on slate shower tiles in middlesex november 30 2019 removing multiple coats of sealer from a dull slate in south yorkshire november 25 2019.
Apply a sealer every three to five years or as recommended by the manufacturer.
Rinse the slate floor with a clean mop and clean warm water.