My in-laws bought my husband a Rockwell soni-crafter for Christmas which came with several blades. I had to go buy a thiner blade to remove the grout.
I have found that our local lowes sells the blades but not the size I needed so I got an adaptor piece to be able to use dremel blades since they have a 1/16 one diamond one. Where the tile is even smaller I am using the blades that are meant for cutting wood.
I have to admit I love it. Where the grout isn't patchy looking, it cuts through like butter. I have trimmed some vinyl flooring at my moms and also cut some door trim higher so I could slide the flooring under it. It was also handy when I needed to cut a piece of 2x4 wood. My brother has borrowed our mitre saw and I hate handsaws. It took a lot longer than using my mitre but it was faster than the handsaws.
The photo shows 75% of the tile I am regrouting. The rest is the "throne" room and the shower. I can't get it in one picture. I can't imagine doing all this by hand.