Gems can be embeded, thus it can also be removed. But the removed gem will lose effect and disappear (with no harm to the equipment). You can also find Charles at the market (92, 99) to do this for you. He will charge you 100,000 gold for every gem removed.

Step 1: Talk to GemSocket Charles at the market (92, 99). Click the gem you want to remove and the button "Remove". (The gem will become shining when you click it. )

Step 2: Gems are precious, please confirm the removing again.