Poorly educated, his father died at the age of 15, and Drew enlisted and fought in the War of 1812. After the war, Drew started a successful cattle-driving business. In 1834, he entered the steamship business, competing unsuccessfully with Cornelius Vanderbilt but running numerous profitable lines outside of New York. In 1844, he founded the brokerage firm of Drew, Robinson & Company in 1844, which dissolved a decade later with the deaths of his partners. He continued to work in the brokerage business as an independent operator.
In 1857, Drew became a member of the board of directors of the Erie Railroad and used his position to manipulate the firm's stock price.
In 1864, Drew once again struggled with Vanderbilt, speculating on the stock of the Harlem Railroad. Drew was selling the stock short, but Vanderbilt and his associates bought every share he sold, ultimately causing the stock price to rise from 90 to 285 in five months. Drew lost $500,000.
In 1866-1868, Drew engaged in the Erie War, in which Drew conspired along with James Fisk and Jay Gould to issue fraudulent stock to keep Vanderbilt from gaining control of the Erie Railroad. Vanderbilt sustained heavy losses and conceded control of the railroad to the trio.
In 1870, Fisk and Gould betrayed Drew, manipulating the stock price of the Erie Railroad and causing him to lose $1.5 million. The Panic of 1873 cost him still more, and by 1876, Drew filed for bankruptcy, with debts exceeding a million dollars and no viable assets. He died in 1879, dependent on his son for support.
Drew, a devout Methodist, built churches in Carmel and Brewster, New York, contributed to the founding of Drew Theological Seminary in Madison, New Jersey, which is now part of Drew University, and Drew Seminary for Young Ladies in his home town of Carmel.