The copy + paste can be done on the Windows Store Whiteboard app. You can't open two instances of the app so, the only way is:
- open the board in the Windows Store Whiteboard app
- Copy what you need (can use Ctrl+A to select all to copy the whole board)
- Go to the Home menu, and choose the existing board or create a new one
- Paste on it. It works!!
Another option, if you need to copy the whole whiteboard: it's on the Whiteboards folder of your OneDrive business account, so you can create a copy in that folder directly.