[1] Graves pitched for most of his career for the Cincinnati Reds, where he was the team's saves leader each year from 1999–2004, except for 2003 when he was a starting pitcher.

After settling in the United States, Graves and his brother, Frank, spoke Vietnamese until teasing from classmates caused them to abandon the language.

As a right-handed relief pitcher for the school as a junior, he posted a 0.89 earned run average and led collegiate baseball with a school-record 21 saves.

In his first nine seasons with Cleveland and Cincinnati, Graves compiled a 40–42 record as a pitcher with 406 strikeouts, a 3.89 ERA, and 172 saves in 755.2 innings.

On April 16, 2004, Graves gave up a milestone and game tying home run to Sammy Sosa in the bottom of the ninth inning.

He pitched well in spring training, earning a spot in the Indian bullpen, but was designated for assignment on May 12, 2006 after he opened the season with a 2–1 record and 5.79 ERA in 13 relief appearances.

[10][11] Graves later signed with the Minnesota Twins on March 30, 2008, and played for the Triple-A Rochester Red Wings most of the year.

[12] He became a free agent at the end of the season and signed a minor league contract with the Houston Astros in January 2009.