If the global variable is already in use, there is no way to copy it to a different event sheet since deleting it will remove all events associated with that variable, and attempting to copy results in duplicate global variable error message.
Specs: Construct 2 r105 64-bit Windows 7 Home Premium 64-bit Intel Celeron
@Kyatric is right - it's not massively intuitive, but it does work. It's difficult to come up with a different way since most people only use one event sheet at a time, so cutting and pasting is the easiest way. And in between it has to hide references to the variable because it doesn't exist until you paste it again!