Removing dried grout from your mosaic is a difficult and messy process. Having done this a few times I'd recommend spending more time on the grouting process and trying to get it right the first time. There are essentially two reasons why you'll find yourself in this situation, the grout has dried before you've had a chance to clean it off properly or your not happy with the grout colour you've chosen. If you need help in choosing your grout colour just click here.
While it is a difficult process there are a few things you can do to make it easier:
Most of all be patient and work carefully, it may be a difficult process but removing the grout is often better than walking away from your mosaic project.
This article has been written based on the assumption that you are removing conventional grout, i.e. cement based grout. If you are using epoxy grout then what I've recommended may not work.