Born in Lewes on September 6, 1781, he was the son of John and Mary Marsh Maull. Choosing to become a physician, he studied medicine with Doctor Jacob Wolfe. By 1803 he had moved to Milton, where he served the medical needs of local residents for the remainder of his life. Doctor Maull's career of public service began when he was appointed to serve as Sussex County Trustee of the Poor in 1810. During the War of 1812 he was a member of the State Militia and participated in the defense of Lewes during the British bombardment in April 1813. Active in the business affairs of the community, he was largely responsible for the construction of the milldam which formed present-day Wagamon's Pond in 1815. In addition to the successful grist mill which was established as a result, he was also the owner of a saw mill and bark mill upstream. First elected to the State Senate in 1816, Maull's record of serve as a member of that body was one of the most distinguished in Delaware during the 19th century. A member of the Whig party, he was chosen to lead the Senate as Speaker in 1845. Next in line of succession, he became Governor of Delaware on March 5, 1846, following the sudden death of Governor Thomas Stockton. Two months later, Governor Joseph Maull also died suddenly at his home in Milton on May 3,. He was laid to rest at St. Peter's Episcopal Church in Lewes.