Mrazek grew up in Huntington, New York, graduating from Cornell University (1967). He joined the United States Navy to serve in the Vietnam War, but was disabled by a training injury at OCS in Newport. After a period of hospitalization with wounded Marines, he turned against the war. Afer his 1968 discharge he was an aide to U.S. Senator Vance Hartke (1969–1971).

He was elected to Suffolk County legislature, 1975–1982 and became its minority leader. He was a delegate to the Democratic National Convention, 1980.

Democrat Mrazek was first elected in 1982 to the 98th United States Congress, defeating John LeBoutillier, a one term Conservative Republican Congressman in the 3rd district. (The districts had been redrawn to reflect the U.S. Census, 1980.)

Mrazek served in the House from 1983 until he retired in 1993. Freshman members usually do not sit on the House Appropriations Committee, but Mrazek persuaded Speaker of the House of Representatives Tip O'Neill to make an exception for him.

Mrazek wote laws to preserve of old-growth forest in Alaska's Tongass National Forest, to protect the Manassas Civil War battlefield in Virginia. He wrote the Amerasian Homecoming Act, which brought home the children of American military personnel from Vietnam, and the National Film Preservation Act, which established the National Film Registry in the Library of Congress. He was proud of legislation to hamper the U.S. Government's ability to intervene in Nicaragua.For his conservation and preservation work, Mrazek was named Conservationist of the Year in 1988 by the National Parks and Conservation Association. He was awarded the Commissioner’s Preservationist Award from the Governor of New York in 1990, and the first legislative achievement award from the Director’s Guild of America in 1987.

Mrazek was caught up in the 1992 House banking affair, in which more than 300 members of Congress cumulatively overdrew their accounts at the House bank more than thirty thousand times over a 39 month period. Mrazek was later the subject of a New York Times editorial titled, “Overdrafts and Overkill,” in which the editors wrote, “Consider the case of Bob Mrazek, the capable Long Island Democrat who was forced to abandon his underdog campaign for the Senate last week. He was cited for 920 overdrafts. Yet he did not bounce a single check. And House bank records show he paid up promptly. This record offers scant basis for a cloud over his reputation.”

Since retiring from Congress, Mrazek has published three critically-acclaimed novels and a well received non-fiction account of Torpedo Squadron 8 in the Pacific War — especially in the Battle of Midway and Guadalcanal Campaign. This work, A Dawn Like Thunder, was named a "Best Book of 2009" (American History) by the Washington Post, and a Notable Book by Naval Proceedings. Stonewall's Gold won the 2000 Michael Shaara Award for Excellence in Civil War Fiction. Deadly Embrace won the 2007 W.Y. Boyd Literary Award "For Excellence in Military Fiction" from the American Library Association.

Adapted for audio (six cassettes), read by Jeff Woodman, Recorded Books, 1999.