Hi. Slate tiles should be sealed before grouting & then again after. Depending on the amount of grout i would use grout remover combined with degrouting pads that topps also have. This is very hard work and time consuming but does normally work. If it does not you can try a brick acid (patio type cleaner) but i would test it on a spare tile first to see if there is discolouration.

hi .best thing i have found is to use wet sand paper not to rough .plenty hot water to clean off .gary gb maintenance uk

Hi have you tried a fine wet and dry paper as it will not scratch the slate too much but grout that has been on slate for this amount or time is very difficult to remove if at all , brick acid is not recommended for a natural stone tile like slate it may cause more harm than good . cheers steve

Depends how much grout is left on the tile first off all, the tile should of been sealed first of all before you layed and grouted the tile, I have used just plan acid watching it down put it over area let it sit for a while you will see it working by the wait it reacts to the grout left over have a hard brush on hand or wet and dry sand paper and rub the area, but remember to have buckets of water to wash down to remember the acid or even a hose to move it all away, iv been doing this for over 10 yrs like this never faulted me, all the stuff you get in shops are strong enough you remove butter from toast.

wet and dry can polish the tiles if the paper is too fine >240 grit,
can leave scratches if too coarse, slate can vary in hardness from very soft, scratch with a fingernail, to something a lot harder,
try a hard plastic scraper or metal one and use it carefully and as the first attempt before sand paper try a green kitchen scouring pad, it will put a nice finish on your tiles(soft to the touch) and no scratches. You can do your whole floor with these if required.
Laying stone tiles seal the stone first and be very clean with your grouting and very thorough with cleaning up behind you