Robert was born on the 20th of February, 1853, on the island of Montserrat in the Caribbean. It was originally stated that he was born in Montreal, Canada, but this was later corrected. He enlisted the US Navy in 1881 in New Jersey and served on the USS Kearsarge. It was his actions when the USS Kearsarge was anchored at Hampton Roads, near Norfolk, Virginia, that would earn him his first Medal of Honor. The citations reads:

Serving on board the U.S.S. Kearsarge, at Hampton Roads, Va., 26 October 1881, Sweeney jumped overboard and assisted in saving from drowning a shipmate who had fallen overboard into a strongly running tide.

Robert received his Medal just six days after saving Seaman E.M. Christoverson and two years later, he was serving on board the USS Yantic. It was docked along side of the USS Jamestown and when a boy had fallen off the connecting plank, both Robert and a Jamestown crewmember, J.W. Norris, displayed actions that would earn him his second Medal of Honor, as well as Norris's first Medal of Honor. The citation reads:

Serving on board the U.S.S. Jamestown, at the Navy Yard New York, 20 December 1883, Sweeney rescued from drowning A. A. George, who had fallen overboard from that vessel.

The citation says that Robert was serving on board the Jamestown but this is because the letter of recommendation for both Robert and Norris was written by the Jamestown's commanding officer. Robert Augustus Sweeney died on the 19th of December, 1890 at the age of 37 and is buried in the Calvary Cemetery in Woodside, New York: there is no record of a burial plot.