Joseph Jordan was born in Manchester on 3 March 1787 the son of William Jordan and Mary Moors. He began his medical education at the age of 15 apprenticed to John Bill (1757-1847), a surgeon at the Manchester Royal Infirmary, but soon began to feel aggrieved by Bill's poor teaching and instead transferred to the tutelage of William Simmons (1762-1830), also on the staff of the Infirmary. Jordan completed his education at the University of Edinburgh, studying under the likes of Charles Bell and Alexander Monro tertius, and qualified with the Royal College of Surgeons of Edinburgh.
In December 1806 Jordan then joined the Royal Lancashire Militia as an ensign and was appointed to assistant surgeon in April 1807, although his only service was reportedly in the Nottingham riots. He left the military in 1811 and headed to London to continue his studies for a year before returning to Manchester to join the private practice of Stewart and Bancks. At the same time he began his first foray into teaching by offering lectures on anatomy from a house on Deansgate. Jordan aspired to open his own medical school as he recognised the poor state of medical education in the country as a whole and considered it unnecessary to expose young men to the moral and social dangers of London. In 1814 he left the practice of Stewart and Bancks and announced in the Wheeler's Chronicle that from October of that year he would be opening rooms on Bridge Street for the study of anatomy.
The lectures quickly became very popular and so the school moved to larger premises on Bridge Street in 1816 before relocating to purpose-built premises on Mount Street in 1826. Although the school relocated he retained his rooms on Bridge Street until his retirement in 1871. Jordan's was the first medical school in the city and his lectures were recognised by the Society of Apothecaries as valid towards the LSA qualification in 1817, although this was withdrawn briefly before being reinstated a few years later. In 1821 the Royal College of Surgeons also recognised his lectures as valid towards the MRCS qualification.
Jordan placed a heavy importance on practical education and the need for dissection and so his school was equipped with anatomy theatres and a substantial anatomical museum. This did not come without controversy and Jordan and his school came under scrutiny on more than one occasion owing to the sourcing of bodies for dissection. On one occasion a rioting mob gathered outside the school and smashed its windows when a cargo of bodies was discovered in a warehouse awaiting transportation to Edinburgh. Jordan seemed to have an ample supply of bodies as it was believed that he was also supplying schools in Edinburgh and London.
Thomas Turner opened a rival medical school on Pine Street in 1824, which is generally seen as the first complete medical school in Manchester, offering the full range of lectures recognised by the leading examining bodies. The two schools continued to operate as rivals for ten years when Jordan agreed to close his school and instead joined the Pine Street School. There had been a number of problems in the run up to the Mount Street School's closure, not least the fact that Jordan's attempts to be elected as surgeon to the Manchester Royal Infirmary were repeatedly blocked. He had put himself forward in 1828 and 1833 and was unsuccessful on both occasions, but had been told he would be successful should he close his Mount Street School and transfer his pupils to Pine Street, and he was duly elected in 1835. He retained this position until 1866. The Mount Street School had run into difficulties some years earlier as well owing to differences of opinion between lecturers and objections to Jordan's nephew, Edward Stephens, assisting so closely in his work.
In 1819, alongside John Hull, William Simmons and others, Jordan had been instrumental in the establishment of the Manchester and Salford Lock Hospital, later St Luke's, for the treatment of patients with venereal diseases who were excluded from treatment at the Infirmary. Throughout his career Jordan campaigned vociferously against the use of mercurial treatment instead favouring iodide of potassium. In 1869 he also became consulting surgeon-extraordinary to the Salford Royal Hospital.
Jordan had passed the exam for the Royal College of Surgeons of England in 1826 and became a fellow in 1843, one of the College's original 300 fellows required for their 1843 charter. He was also an active member of a number of organisations and was an original member of council of the Manchester Medical Society, a founding member of the Chetham's Society, and also served as vice-president of the Manchester Royal Institution in 1857.
Ill-health saw Jordan retire from practice in 1871 and he died in London on 31 March 1873.