Without getting into a flaming war, I agree that a tile cutter
is perfect
for cutting straight lines in tiles, it's what I used for 95%
of the cut
tiles in our bathroom. However it is crap for cutting curves,
intricate
mouldings and cutting sections from the centre of a tile. It's
horses for

Actually, you can do a good job of moderately intricate shapes
with a table saw type cutter.

Draw the shape on the tile surface. Run a scribe over the line.
Cut at 90 degrees to the line, dividing the waste into a series
of fingers cut just short (about 0.5 - 1mm) of the line. Keep
dividing the fingers so they get thinner and thinner. Eventually
they either snap off or you can take them off near the base with
a slight sideways movement of the tile. You can then tidy to
within a hairsbreadth of the line using the cutter to nibble off
the high points.

The final step is to use abrasive paper, rolled into a tight
cylinder if necessary.

It ain't fast, but it's fast enough for a few tiles. It takes
fine control and close observation (wear safety specs) but it's
do-able and the results are good, especially when you've done a
few.

No help to the OP though.

W.