He attended High Holborn Academy in London, England and then studied law, graduating from Eton College in 1859.

Elliott helped organize the local Republican Party and served in the state constitutional convention in 1868 as a delegate from the Edgefield district.

The next year he was appointed assistant adjutant-general; he was the first African-American commanding general of the South Carolina National Guard.

As part of his job, he helped form a state militia to fight the Ku Klux Klan.

[3] Elliott was elected as a Republican to the Forty-second United States Congress, defeating Democrat John E. Bacon.

[8] He continued to be involved in politics, working on then-Treasury Secretary John Sherman's campaign for President in 1880, and was a delegate to the 1880 Republican National Convention.

In January 1881 he was part of a black delegation that met with President James Garfield to protest the lack of civil and political rights in the South.