Here I have IDT's P9025 A/C wireless power receiver board, and I'm going to show you how to separate the active circuit area from where the coil is mounted.
The first thing you'll need to do is remove the coil from the board, and I've already done that. You de-solder the leads and pry it off the board. And you'll notice this board is scored right here between the two parts, allowing you to break it in two. You might want to do this if you're planning to prototype with the board, and you need something a little bit smaller to fit inside of your design, and also plan to put the coil somewhere different than where the active circuit is located at.
The score line is located right here, so just put it on the edge of the table. Put your palm on the active circuit area and press down on the other half the board, and it will separate in two. Now that you've separated your board, you don't need this anymore, and you're left with a smaller board that is easier to put inside of your prototype.