I have damage to my ceramic tile patio where water has seeped in underneath the tiles and caused them to raise about an inch. I need advice on the best way to try to remove them without breaking them since I can't find replacement tiles. Is the first step to chip out the grout around the edges?..If so, how do I loosen the adhesive underneath. Part of it has obviously already broken away in the rising?...Help please.

Cut out the grout with a grout saw.You can find them at any home improvement store. A razor knife might also work if the grout is weak enough.
Put a wide flat chisel as far under the tile and as flat against the floor as you can. Then begin slowly tapping with a hammer getting a little harder as you need to. It will either pop off the floor in one piece or it's going to snap.
This may not be salvagble.
Where's the water coming from?

Thanks for the suggestions. We don't know where the water is coming from. Need to remove the tiles first to determine the source.

A hammer and chisel also can work. Hope you solve the water issue!