A member of the Democratic Party, he served as the United States representative for Ohio's 1st congressional district from 1993 to 1995.

Mann ran in the 2021 Cincinnati mayoral election, but lost to Hamilton County Clerk of Courts Aftab Pureval.

At the time of his birth, Mann's parents resided in Park Hills, a Northern Kentucky suburb of Cincinnati.

[1] Mann completed his secondary education at Dixie Heights High School[2] before attending Harvard University on a Navy ROTC scholarship, graduating cum laude in 1961 with a degree in biochemical science.

Mann was term-limited in the City Council and was considering a campaign for a judicial position, but instead decided to run for the congressional seat, stating that his name recognition would help propel him to victory.

Mann won the three-week special primary to become the Democratic nominee, narrowly defeating State Senator William Bowen.

[16] After learning that one of his sons was gay, he voted in favor of Barney Frank's failed 1994 bill to prohibit anti-LGBT discrimination.

[17] Mann voted in favor of the North American Free Trade Agreement, which damaged his reputation with some of his allies in organized labor.

Unions were divided on Mann's general election campaign; some, such as the Ohio Education Association, endorsed him, while others, such as the Cincinnati AFL–CIO Labor Council, refused to do so.

[23][24] Mann opposed the Cincinnati streetcar and voted to halt its construction on his fourth day in office, but work on the project eventually proceeded.

[27] That same year, Mann proposed levying an excise tax on short-term rentals, with the proceeds going to the city's affordable housing fund.

In a letter to potential donors, Mann stated that he had no ambitions for higher office beyond city politics and that his "experience and leadership qualities" could help address the effects of the COVID-19 pandemic.

[1][6] Mann has served on the boards of numerous charitable organizations, including the Make-A-Wish Foundation and the Freestore Foodbank.