Richard Caswell was born in the seaport of Joppa, Maryland, on August 3, 1729. He lived with his parents and siblings at the family plantation of Mulberry Point and attended his early schooling at a local Anglican parish school taught by the Reverend William Cawthorne and the Reverend Joseph Hooper. In 1746, Richard’s father’s merchant business began to suffer. This prompted Richard and his older brother William to leave Maryland and travel to North Carolina, carrying with them a letter of recommendation from the Royal Governor of Maryland to the Royal Governor of North Carolina, Gabriel Johnston. The brothers were to find work and a future home for their family, who would end up joining them two years later in 1748. After arriving in North Carolina and at the age of only 17, Caswell was appointed as an apprentice to Surveyor General James Mackilwean, where he learned the art of surveying. This was a very profitable trade in the Eighteenth Century; Surveyors would purchase newly opened land as the frontier expanded and sell the tracts to settlers at higher prices. Colonists held surveyors in suspicion, but Caswell remained popular with the people throughout his political career. Today, students visiting the Richard Caswell Memorial can experience eighteenth-century surveying with a hands-on activity with authentic instruments.

Caswell's career landed him in numerous government offices and eventually into the Colonial Assembly, which operated as the North Carolina legislature under British rule. At the age of 18 in 1748, Caswell was appointed Deputy Clerk of Johnston County. Quickly after in 1750, he was made Surveyor General. Caswell presented a bill to establish the town of Kingston, North Carolina's 20th official town, and utilized his knowledge of surveying to plan the town layout. Caswell Street in present-day Kinston links the streets' names to honor the families of his wives; Mackilwean Street for the family of the then-deceased Mary Mackilwean and Herritage Street for the family of his then-current wife, Sarah Heritage. In 1784, after the Revolutionary War ended, Caswell helped to implement the new town name of Kinston, rather than Kingston, to sever ties to its namesake, King George III.

When the relationship between the British government and the American Colonies became further strained, Caswell attended the First Continental Congress in 1774, followed by the Second Continental Congress in 1775. John Adams said of Caswell, "We always looked to Richard Caswell for North Carolina. He was a model man and a true patriot." Royal governor Josiah Martin held a less flattering opinion of him, calling him "the most active tool of sedition." Caswell presided over the Fourth Provincial Congress in 1776, preventing him from participating in the famous drafting and signing of the Declaration of Independence. In November of the same year, Caswell presided over the committee that drafted the state Constitution in the Fifth Provincial Congress. He was first appointed acting governor in December of 1776, followed by his election as governor by the First General  Assembly in January of 1777. This was the first of three one-year terms. During this time, he also entertained the Marquis de Lafayette and Baron Johann de Kalb in New Bern. 

After the Revolutionary War, Caswell served North Carolina as Controller General (Treasurer) and faced the difficult task of settling the state's post-war finances. He served again as governor for three one-year terms between 1785-1788. During the term of Caswell's predecessor Alexander Martin, North Carolina territories west of the Blue Ridge split from the state and formed the new state of Franklin, founded by John Sevier. While Governor Martin had pursued an aggressive policy of intimidation, Caswell was more diplomatic towards the "Franklinites." Through delicate negotiations and peacekeeping, he persuaded the territories west of the Blue Ridge to reunite with North Carolina, preventing a civil war. The western territories would eventually become the state of Tennessee, with John Sevier becoming the new state's first governor. 

Illness prevented Caswell from participating in the 1786 Constitutional Convention, and William Blount—who favored the adoption of the Constitution over the Articles of Confederation—was sent in his stead. In 1789, Caswell was elected Speaker of the Senate in the North Carolina Assembly. On November 5 of the same year, he suffered a stroke while in session at Fayetteville and remained bedridden before dying five days later on November 10, 1789. A funeral service for Caswell was held soon after in Fayetteville, and it is believed that his body was then transported to Kinston, North Carolina, for burial.