Nelson Grubbs was in the 1st Cherokee Mtd Rifles (Confederate), aka Drew's Regiment. He was in Co. G, Capt Albert Pike's company (not to be confused with Brig Gen Pike) and enrolled in Tahlequah District -- age 22.
This regiment defected in June/July 1862 and filled the ranks of the 2nd Indian Home Guard plus created 3rd Indian Home Guard (Union), aka the Pin Regiment.
He does not show up on the rolls of the 3rd IHG so there is no record I can find of his death. There is a pension record that appears to say his unit was the 3rd Indian Home Guard Regiment and apparently applied for by his wife, Sarah Wofford.
While he may have been killed in combat, there are a higher number of deaths from disease so that is also a possibility. A listing at http://www.genealogy4all.org/FtGCem.html says he was originally buried at Park Hill and apparently moved to the National Cemetery at a later date.