[2][3][4] Born either in Mathews County[5] or Fredericksburg, Virginia,[6] to Carter Moore Braxton Sr., Elliott lost his mother as child.

[13] As Virginians voted to secede from the Union at the outbreak of the Civil War, Braxton enlisted as a private, then raised a company in Stafford County for the Confederate Army.

In August 1862 Braxton was promoted to a major and assigned as brigade quartermaster on the staff of General John R. Cooke, despite an attempt to obtain an army judicial post in the autumn of 1864.

He had his legal disability removed and won election to Fredericksburg's common council in 1866; the state's government was reorganized in 1868 due to Congressional Reconstruction.

[15] Following redistricting, Braxton ran in the 1st district against Republican lawyer and newspaperman James B. Sener, this time losing by a narrow margin of 49-51% (373 votes).

He moved unsuccessfully to compensate the Lee family for Arlington plantation the federal government had seized during the Civil War.