Cuthbert was born in Savannah. He was instructed by private tutors and graduated from Princeton College in 1803. He studied law and was admitted to the state bar about 1805 but did not practice.
He was not a candidate for renomination in 1826, but was elected as a Democrat to the U.S. Senate to fill the vacancy caused by the resignation of John Forsyth; he was reelected in 1837, and served from January 12, 1835, to March 3, 1843. Cuthbert was not a candidate for reelection in 1843, and retired from active business pursuits and lived on his estate near Monticello in Jasper County until his death in 1856; interment was in Summerville Cemetery, Augusta, Georgia.