Tile – Detaching large ceramic tile without breaking it

For cutting porcelain or ceramic tile, standard practice is to use:

• A wet saw with a diamond blade
• A manual tile cutter (a carbide wheel slides along a rail to score the tile, then you snap on the line.
• Tile nippers for complex shapes

You can use a diamond blade with a hacksaw to cut holes, but it won't be very efficient.

If you have mostly straight lines, you can get away with a decent manual cutter and perhaps a pair of nippers. A wet saw makes the job go faster, but is not necessary.

This looks more like a cracked tile than a scratch (but it is difficult to say from the picture). Was there work done after the tiling that may have put stress on the wall? I must admit that it is unusal to see this on a wall tile. Replacing it is not rocket science and the preferred method (there is really no other way to fix this).