What is the best method to cut 'Mother of Pearl' super thin seashell tile?
With a small tile like this I would snap it off.

First, scribe the tile with a carbide scribe line where you want it to break.

Next, use a glass cutter to make a groove along the line with the help of a square or a ruler.

Put the tile in a vise with wooden jaws or otherwise clamp it securely.

Snap off the excess with a pair of pliers.