Murphy was nominated by President Jimmy Carter on November 30, 1979, to the United States District Court for the District of Minnesota, to a new seat created by 92 Stat. 1629. She was confirmed by the United States Senate on February 20, 1980, and received commission the same day. She served as Chief Judge from 1992 to 1994. Her service was terminated on October 13, 1994, due to elevation to the Eighth Circuit.[2]
Murphy was nominated by President Bill Clinton on July 28, 1994, to a seat on the United States Court of Appeals for the Eighth Circuit vacated by Judge John R. Gibson. She was confirmed by the Senate on October 7, 1994, and received commission on October 11, 1994. Upon assuming office, Murphy became the first woman to serve on the Eighth Circuit.[2][4]
Murphy assumed senior status on November 29, 2016. She died in her home in Minneapolis on May 16, 2018, shortly after announcing her full retirement from the bench.[5] Later that year, the Minnesota Law Review hosted a memorial symposium in her honor, which included contributions from Justice Ruth Bader Ginsburg, Judge Michael Joseph Melloy, and Judge Rubén Castillo.[6]
After her death, the United States federal courthouse in Minneapolis was renamed in her honor.[7][8]