Joseph was born on the 4th of June 1864, in Boston, Massachusetts, where he also enlisted in the US Marine Corps in August of 1888, at the age of 24. He was a Private on board the USS Nashville when he deployed to Cuba in support of the Spanish-American War, and his actions during the Battle of Cienfuegos later earned him the Medal of Honor. The citation reads:

On board the U.S.S. Nashville during the operation of cutting the cable leading from Cienfuegos, Cuba, 11 May 1898. Facing the heavy fire of the enemy, Scott displayed extraordinary bravery and coolness throughout this action.

Joseph received the Medal of Honor on the 7th of July 1899, and he remained in the Marines, reaching the rank of Corporal, until May of 1901. Unfortunately, not much else is known about his life and Joseph Francis Scott died on the 28th of February 1941, at the age of 76 and he is buried in the Cambridge Cemetery in Cambridge, Massachusetts: Mayflower Path, Lot 4716B.