Joseph E. Broadwater was born in Accomac County, Virginia to David and Mary Ann White Broadwater on April 29, 1837. He prepared for college at academies in Drummondville, Virginia and Bel-Air, Maryland before entering Dickinson College in Carlisle, Pennsylvania in 1854. Broadwater was elected to the Belles Lettres Society and graduated with his class in July 1858. He then studied medicine at the University of Maryland and was awarded the M.D. there in 1860.
Broadwater returned home to Virginia's Eastern Shore and took up practice in Temperanceville, Virginia. He spent the remainder of his life there as a family physician. Broadwater was also elected to a term in the Virginia House of Delegates in 1889, and he served as a member of the school board for Accomac County.
Broadwater married Elizabeth Ann Justice in 1860, but she died in August 1862 at the age of twenty-two. Two years later, he married Elizabeth Whatnot Taylor, and the couple had twin sons, David and Edward. Within a year, both mother and one twin, Edward, were dead. Elizabeth died in February 1866 while still only twenty. Throughout his life, Broadwater's surviving twin son, David, spent periods in a hospital for the insane. In July 1868, Broadwater married Mary Elizabeth Oldham of Northampton County, and the couple had three children: Mary Inez, Carrie Proctor, and Joseph Royall. After long service to the town of Temperanceville, Joseph Emory Broadwater died there on February 24, 1899. He was buried with his first two wives and his son in the J. W. Taylor Cemetery. Broadwater was sixty-one years old. His third wife survived him.