Post this on the john bridge tile forums. In addition to the answer, you might get some valuable feedback on why it might not be such a good idea, looks-wise.

I think a grinder with a wet/dry diamond blade would do it.

You can use your wet saw sort of like a grinder to round off the edges and even cut a few nicks out of the edges of the tile, but you gotta be really careful. You don't want to bind up the saw blade, or cut off a finger or have a chunk of tile fly in your eye. Maybe a dremel tool would work with the right grinding wheel attachment - but you might burn up the motor before you got too many tiles done. Good luck!

One of the many reasons cut edges of tile are normally 'buried' at the edge of the field where they cannot be seen.

The only edges left in a filed are square cut edges on square cut tile (or stone).

It is often a problem with MANY tiles since they often have a slight rounded edges down to the grout joint, and unless they are a solid tile (same finish all the way through) the square edge sticks out like a sore thumb in a field of rounded edge.