The county recorder's office where your ancestor lived after his military discharge may have a registered copy of his discharge papers. Military men were encouraged--especially during the American Civil War era and after, to have a copy of their military discharge recorded at their local county recorder's office.
Could be a good place to get a copy of the record. Records for discharges during World War II and after are probably some type of photoreproduction of the document. Earlier ones are most likely handwritten transcriptions.