Grouting slate floor tiles

So far it sounds like you have done everything right, all you have left now is grout water residue. As long as the heavy clumps of grout have been removed & 99.9% if the grout is off the surface then you are ok to give the floor a final coat of sealer.

For the inexperienced DIY'er fitting a slate floor for the 1st time this would look quite worrying but it is completely normal. The final coat should Overseal the residue & make it disappear leaving a beautiful looking finished slate floor.

Again our advice would be to try a test area before proceeding.