Spills and stains that are allowed to soak into unsealed stone can permanently mar slate tiles, and the problems can start with the installation process itself. Grout that is allowed to dry on the surface of unsealed slate creates a haze over the tiles and can be very difficult -- and sometimes impossible -- to remove. Always apply a stone-sealing or grout-release product to slate tiles before grouting. If you are having a contractor install the slate for you, ask how he plans to protect the tiles and insist he seal them before the grouting portion of the project begins. A good tile installer will always protect porous stone surfaces and should not need any persuasion. There are several grout haze removal methods that you can try before declaring the floor permanently scarred. Always start with the least potent methods and work your way up to potentially harsh chemical options.
Scrape away any high spots and hunks of dried grout with a squared-off block or stick made of oak wood. Wear a pair of work gloves while you do this to prevent splinters. Vacuum the floor to remove any of the grout you were able to scrape away.
Scrub the tile with a nylon brush or scrubbing sponge and a bucket of warm water. Wipe the cleaned area with a grout sponge to take up the excess water after cleaning, and then wipe the area dry with a clean towel. Work in small sections so you can easily see whether or not the water is working. If it is, continue cleaning the floor in this manner. If it is not, dry the floor and move on to the next cleaning method. You will need to change the water in the bucket frequently to keep it clean.
Dissolve 1 cup sugar into a gallon of warm water. Pour the solution over the floor and let it sit for two hours. Scrub the floor with a nylon brush or scrubbing pad to remove the grout haze, and vacuum the sugar water up with a wet/dry vacuum. Mop the floor with clean water as a final rinse to remove any sugar residue. You can repeat the process if the sugar water removed some but not all of the haze.
Wait 72 hours for the grout between the tiles to completely set and then apply a commercial grout haze removal product to the slate. Apply the chemical to the slate, scrub with a nylon pad or brush, and then rinse the product away with a damp cloth or mop within 10 minutes of application. Always read the label on grout removal chemicals before using to make sure the product is safe for slate, and follow the directions on the label. Some products may need to be applied differently or left on the slate for a specific amount if time. Wear gloves, safety goggles and any other protective equipment the grout removal manufacturer recommends.
Call a professional if you still have haze to see what he recommends. Be aware that, depending upon the type of grout used and severity of the problem, replacing the new floor may be the only way to fix it.