Would I have to deactivate my current Windows 8 license key, pop in the upgrade disc and reinstall?
No, you don't have to reinstall. You might have to reactivate, possibly over the phone, but other than that you can just do the hardware upgrade and continue using your Windows 8 installation.
Of course, this assumes that your machine currently has a retail version of Windows. If your current licence is an OEM one, then it's tied to the motherboard it was bought with or first activated on. So if you buy a new motherboard, you'll have to get a new licence of a previous version of Windows in order for your computer to remain eligible to use the Windows 8 upgrade licence.
Or does the disc/license key become junk because I already used it once for an upgrade therefore I do not have to use it again?
No, the licence key does not become useless after being used once. You can use it on another machine, provided you first deactivate it on the first one.
Or would I have to reformat the drive, install my previous version of windows, then pop in the same upgrade disc after upgrade my motherboard?
Also no, there's no need for reinstallation. You can do it, of course, and may want to so as to start from a clean slate with no leftover drivers from the previous motherboard (depends on how different they are), but that's entirely up to you.
Can someone can tell me how it would work (or if its even possible) for me to reinstall WIndows 8 after running an upgrade? Or if its possible to deactivate my upgrade on one machine to upgrade another?
Yes, you can deactivate your Windows 8 upgrade licence. All you have to do is reinstall the previous version of Windows that you upgraded from. Or even just wiping the drive will do. After that you can use the Windows 8 licence to upgrade another eligible computer.
You can check out the Windows 7 and Vista Activation FAQ here on SuperUser, there's a lot of useful information there, most of which should apply to Windows 8 as well.