Coppersmith graduated magna cum laude from Harvard, and then worked as a Foreign Service Officer with the U.S. State Department, assigned to the U.S. Embassy in Port of Spain, Trinidad. He then earned a law degree from Yale Law School. After law school, he clerked for Judge William C. Canby, Jr., of the U.S. Court of Appeals for the Ninth Circuit, and served as an assistant to the Mayor of Phoenix.

Coppersmith defeated John Rhodes III in his 1992 campaign. While serving in Congress, he kept a campaign promise by returning a congressional pay raise he opposed by writing a check each month to the U.S. Treasury. Coppersmith also gained national attention with his leadership of the effort to eliminate the Advanced Liquid Metal Reactor program, an effort that united a coalition of budget-cutters, environmentalists, and foreign policy experts concerned about plutonium. Also, through his efforts, the U.S. Department of Labor and Department of Education talked with each other to end an interpretation of labor laws that kept parents in some Arizona schools from participating in their children's classrooms.

Coppersmith ran unsuccessfully for the U.S. Senate in 1994 when Dennis DeConcini retired. He lost to fellow Congressman Jon Kyl.

After leaving Congress, Coppersmith spent two years as the chairman of the Arizona Democratic Party. He is currently an attorney specializing in real estate law, and a managing partner of the law firm of Coppersmith Gordon Schermer Owens & Nelson P.L.C.