Joseph was born in Huntsville, Alabama on July 6, 1816 to Samuel Black and Elizabeth Hunt Acklen. His grandfather, John Hunt, was the founder of Huntsville. Both the Hunts and the Acklens were early settlers in northern Alabama.
At the age of 14, Joseph enrolled in the first class offered by the newly established University of Alabama. Most of his 51 classmates would become important early leaders in the state. Joseph attended school there for four years, receiving a classical education in Greek, Latin, and history. Although an essay book he used while at the university survives today, there is no record of his graduation. However, he did receive an interest in architecture.
When the Texas Revolution began in 1835, Joseph, along with other young men from Huntsville went west to fight under Capt. Peyton Wyatt. His company was assigned to Col. James W. Fannin, Jr., who was executed along with most of his men at Goliad, Texas, on March 27, 1836. However, Joseph's company escaped the massacre, having already left Texas to return home.
After the war, President Martin Van Buren appointed Joseph the United States Attorney for the North Alabama Judicial District in 1840. Prior to his appointment, he probably studied law in Huntsville with his older brother, William. During his time as a US Attorney, Joseph also operated a law practice with his brother. While visiting Nashville in April, 1847, Joseph attended a ball given by Mr. and Mrs. John Bell where he met the recently widowed Adelicia Franklin. Two years later, Joseph resigned from his position as US Attorney and moved to Nashville to marry Adelicia.
Joseph arrived in Nashville on May 1, 1849, and checked into the Sewanee House Hotel along with his brother Mr. A. A. Acklen and Mr. E. H. Betts. On May 6, another group of people arrive from Huntsville for their marriage on May 8. However, one day before their marriage, Adelicia asked Joseph to sign a marriage contract stating that she would retain ownership and control of all the property she brought to the marriage. He agreed. The following day they married at her home on Cherry street. Dr. John Edgar, pastor of the Presbyterian Church, officiated at the ceremony. Attendees included former President James K. Polk and Mrs. Polk. It is assumed the couple left for a wedding trip soon after, but it is not clear where they went. However, they do end up in New Orleans on November 6th.
After their marriage Joseph assumed the management of Adelicia's property. After Isaac Franklin's death this had been the legal responsibility of her father, Oliver Bliss Hayes. Construction began at Belmont in October 1849. Construction would last about three years; the family moved into Belmont in the late summer or early fall of 1853. In the following years, construction continued at Belmont, both with additions to the house as well as the building of various structures on the grounds. The pursuit of building and architecture appears to have been Joseph's interest as after his death Adelicia only adds one more building.
Despite his appointment as a US Attorney in Northern Alabama, Joseph never holds elected office in Tennessee or Louisiana, perhaps because he was only a part-time resident in both states. He was, however, involved in the Tennessee Democratic Party. He attended the Democratic National Convention in 1856, and was a representative of Louisiana at the Southern Convention of 1857 in Knoxville, Tennessee.
When Tennessee seceded from the Union and war was declared, Joseph paid for the outfitting of a company of soldiers. In February of 1862, Fort Donelson, which was upriver of Nashville, fell to the Union army. The Confederate army made no attempt to defend the city so Joseph, along with about a third of Nashvillians, fled the city. Joseph went to Louisiana to manage their plantations while Adelicia remained at Belmont.
The next year and a half was harrowing. The location of the plantation on the Mississippi River at the mouth of the Red River was a prime spot for the crossing of Confederate troops, yet the river was controlled by Federal gunboats. Because of the proximity of both armies, the cotton bales stored at all of the couple’s Louisiana plantations were in constant danger of being burned or confiscated. Both armies would rather destroy the cotton then have the other side benefit from its sale. By the summer and fall of 1863, the Confederate army was threatening Joseph for not burning his cotton, which by now amounted to 8,500 bales of cotton. The Federal army offered to protect him, but Joseph refused for fear of retaliation by renegade Confederate soldiers in the area. Eventually, against his will, the Federals did provide protection. By August of 1863, Joseph was disillusioned, tired, sick, and apparently so arthritic he was unable to write. In a dictated letter to Adelicia sent on August 20th, he said the south had no chance of winning the war. Slavery was finished and he was glad of it.
On September 11, 1863 at the age of 47, Joseph died on the Angola Plantation from what a newspaper called “bilious remittent fever” or malaria.