The below information came from the Medical and Surgical History of the War of the Rebellion.

“Private Martin, (or Martis) of the 26th Brooks’s Arkansas Regiment, aged 25 years was wounded at Prairie Grove, December 7, 1862, by a cannon shot which shattered his left thigh so dreadfully as to leave the limb attached to the trunk only by the soft parts on the anterior aspect. His case had been regarded as hopeless but after the surgeons had finished all of the other operations he was observed to have rallied somewhat, though greatly exsanguinated and prostrated. With the assistance of Drs. Duvall and Keller, Surgeon W. B. Welsh, P.A.C.S. of Gunter’s Arkansas Regiment performed exarticulation, making a large anterior flap. The operation was performed twenty four hours after the injury and the patient survived four days, when he succumbed from exhaustion.”

Although it's a stretch one candidate may have been Matthew Mathis of Company G of the 26th Arkansas Infantry.