Zemurray's original name was Schmuel Zmurri. He was born in Kishinev, Bessarabia, Russia (present-day Chişinău, Moldova) to a poor Jewish family that emigrated to America when he was fourteen years old. Zemurray had no formal education. He entered the banana trade in Mobile, Alabama in 1895, at the age of eighteen. His early wealth was largely due to a very successful venture in New Orleans, Louisiana, where he bought the bananas that had ripened in the transport ships and then sold them locally. His success earned him the nickname "Sam the Banana Man." By age twenty-one he had banked $100,000. He later bought a steamship and went to Honduras. In 1910, he bought 5,000 acres (20 km²) of land along the Cuyamel River. He later added more land and found himself heavily in debt.
Honduras and Nicaragua at the time were working to reschedule their debts. United States Secretary of State Philander C. Knox was involved in the negotiations, which would have agents of bankers J.P. Morgan and Company sitting in the countries' customs offices to collect the taxes needed to repay the debt. Zemurray feared that he would be taxed out of business and appealed to Knox for help. Knox spurned him so he returned to New Orleans, where deposed Honduran president Manuel Bonilla was living. Zemurray smuggled Bonilla back to Honduras and a revolution was fought that led to Bonilla's return to power. Bonilla granted Zemurray land concessions and low taxes that saved his business.
In 1930, Zemurray sold his company, Cuyamel Fruit, to the rival United Fruit Company of Boston, Massachusetts for $31.5 million in stock and retired. But the company suffered because of mismanagement and the Great Depression. The stock plunged 90% from when he sold, so Zemurray returned to the business in 1933 by voting out the board of directors. Zemurray reorganized the company, decentralizing decision-making and made the company profitable once more. In 1951, Zemurray authorized Edward Bernays to launch a propaganda campaign against Jacobo Arbenz, democratically-elected president of Guatemala. He retired as president of United Fruit later that year.
Zemurray and his family made generous donations to Tulane University, Zamorano, and to other philanthropic ventures, including the Zionist movement through his personal acquaintance, beginning in the 1920s, with Chaim Weizmann. Zemurray supported President Franklin D. Roosevelt's New Deal policies, helping to draft the Agricultural Adjustment Administration industry codes , and contributed financially to left-wing causes such as The Nation magazine He created the Zemurray Foundation in 1951. His former mansion on Audubon Place is now the residence of Tulane's president. His daughter, Doris Zemurray Stone, an archaeologist and ethnographer, served as the director of the National Museum of Costa Rica and endowed various professorial chairs in U.S. universities.
Zemurray died in New Orleans, where he had lived for most of his life.