Joseph Titcomb was born on June 8, 1822, in Kennebunk, Maine, the son of James and Abigail Titcomb. Little is known of his childhood, but Titcomb attended Bowdoin College from 1839 to 1843, after which he briefly studied law. Rather than pursue law, he decided instead to enter the shipping business, wherein he was quite successful. He married Mary Wise in December 1852.
Titcomb took an interest in public affairs and service, serving as a member of the Maine state Senate (1849-1852), state House of Representatives (1852), and trustee of Bowdoin College (1868-1891). Joseph Titcomb died on December 26, 1891. Joseph and Mary had two surviving children, Agnes (b. ca. 1860) and William (b. ca. 1863).