Been there, done that, I feel your pain.
The muppet who did this, believe it or not, was a professional tiler. *sigh*
Bunnings sell a grout removal bit for a dremel, which works a treat. It's expensive, $30 or so, but also rips through tiles. Which is important when you try to get the tap out, as in my case the hole in the tile wasn't big enough for the tap body.
Fun and games. Good luck.