Joseph Cunard was born in 1799, in Halifax, Nova Scotia.

He was a merchant, shipbuilder, and politician, a brother of Samuel Cunard (1787-1865). After completing his educated in Halifax, he entered his father's firm. Around 1820, with his brothers Henry and Samuel, he opened a branch of the family timber business in Chatham, New Brunswick. The firm operated mills, wharves, a store, and shipyards and later expanded into investments in shipping. In 1832, he was described as one of the wealthiest men in the province. Cunard was also a justice of the peace and served on the board of health for Northumberland county. Having entered politics in 1828 as a Member of the Legislative Assembly (MLA), he was appointed to the Legislative Council in 1833 and sat on the Executive Council from 1838 to 1846. His bankruptcy in 1847 left hundreds out of work. His brother Samuel took out loans and personally guaranteed all his brother's debts in Nova Scotia, New Brunswick, and Boston. Joseph moved to Liverpool, where he entered the commission business, purchasing supplies for colonial merchants and selling their ships and lumber.

In 1833, he married Mary Ann Sharman Peters (1816–1884). He died on January 16, 1865, in Liverpool, Lancashire, England.