Dexter was born in Malden, Massachusetts. He had little schooling and worked as a farm laborer at the age of 8. When he was 16, he became an apprentice to a leather-dresser. In 1769, he moved to Newburyport, Massachusetts. He married Elizabeth Frothingham, a rich widow, and bought a mansion. Some of his social contemporaries considered him unintelligent. Many of them gave him bad business advice to discredit him and make him lose his fortune.
At the end of the American Revolutionary War he bought large amounts of depreciated Continental currency that was worthless at the time. After the war was over, the U.S. government made good on the dollars. By the time trade connections resumed, he had amassed a fortune. He built two ships and began an export business to the West Indies and to Europe.
Because he was largely uneducated, his business sense was considered peculiar. He was inspired to send warming pans (used to heat sheets in the cold New England winters) for sale to the West Indies, a tropical area. His captain sold them as ladles for the local molasses industry and made a good profit. Next, Dexter sent wool mittens to the same place, where Asian merchants bought them for export to Siberia.
People jokingly told him to "ship coal to Newcastle". He did so during a miners' strike at the time, and his cargo was sold at a premium. At another time, practical jokers told him he could make money shipping gloves to the South Sea Islands. His ships arrived there in time to sell the gloves to Portuguese boats on their way to China.
He exported Bibles to the East Indies and stray cats to Caribbean islands and again made a profit; eastern missionaries were in need of the Bibles and the Caribbean welcomed a solution to rat infestation. He also hoarded whalebone by mistake, but ended up selling them profitably as a support material for corsets.
Members of the New England high society rarely socialized with him. Dexter decided to buy a huge house in Newburyport from Nathaniel Tracy, a local socialite, and tried to emulate them. His relationships with his wife, daughter, and son also suffered. This became evident when he started telling visitors that his wife had died (despite the fact that she was still alive) and that the woman who frequented the building was simply her ghost. In one notable episode, Dexter faked his own death to see how people would react. About 3,000 people attended Dexter's mock wake. Dexter did not see his wife cry, and after he revealed the hoax, he caned her for not grieving his death sufficiently.
Dexter also bought an estate in Chester, New Hampshire. He decorated his house in Newburyport with minarets, a golden eagle on the top of the cupola, a mausoleum for himself and a garden of 40 wooden statues of famous men, including George Washington, William Pitt, Napoleon Bonaparte, Thomas Jefferson, and himself. It had the inscription, "I am the first in the East, the first in the West, and the greatest philosopher in the Western World".
At age 50, Dexter authored A Pickle for the Knowing Ones or Plain Truth in a Homespun Dress, in which he complained about politicians, the clergy and his wife. The book contained 8,847 words and 33,864 letters, but without punctuation and seemingly random capitalization. Dexter initially handed his book out for free, but it became popular and was reprinted eight times. In the second edition, Dexter added an extra page which consisted of 13 lines of punctuation marks with the instructions that readers could distribute them as they pleased.
Dexter's Newburyport house became a hotel. Storms ruined most of his statues; the only identified survivor was that of William Pitt. His book remains his primary legacy to this day.