What is the problem here? You want the stream to only hear the game and your mic input while running mumble in the background?
Mumble is part of the system sounds and that is the source that OBS is picking up. You could deactivate the system sounds in OBS and only pick up your mic or - and this is an assumption on my part - you could install a dedicated sound card running your game sounds through it and then picking it up via OBS.
You can also look into VAC (virtual audio cable) to help with this issue, I am very unfamiliar with the hows on this but im sure there is a subject matter expert out there via the forums of a google search
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