We just purchased a bank owned home, it is 8 years old. The master bath shower is all tiled with natural stone and granite tiles. The downstairs ceiling showed some old water stains. While doing some upgrading before we moved in I turned the shower on and let it run didn't seem to be a problem,no leaks. Then I tried putting a drain plug in and filling up the bottom of the shower with 1 inch of water. Within a minute all the water was downstairs through a canned light socket in the kitchen. I have removed the grout around two 4 x 4 stone tiles and was able to pop of the tiles (took a little work but not much). I don't think it should be that easy to remove tiles without doing damage to them.
Where should I go from here?

Before I removed any tiles I would remove the drain lip and replace the putty seal, (see image). If that seal were ruptured it would give you the situation that you have.
Remove the strainer and drain lip. You may roll a small rope of plumbers putty or use Silicon Jel for a seal. After you replace the seal block off the drain and fill the base again to test. Did that cure your leak? Good luck, Tom