Graves was born in Tarkio, Missouri and he graduated from the University of Missouri. Graves was elected to the Missouri House of Representatives in 1992 as a Republican and he was then elected to the Missouri State Senate in 1994.

In 2000, Congresswoman Pat Danner suddenly retired due to breast cancer. Graves filed within the short period of time left for filing. Graves faced Congresswoman Danner's son, Steve Danner, a fellow state lawmaker, in the general election. Graves referred to Danner as a "tax and spend Liberal" and won the race with 51f the vote . Graves easily won re-election in 2002 and 2004 .

Because Missouri's 6th District has changed between Democratic and Republican control several times, elections in the district tend to be closely contested. As a result, candidates in the district often receive large conributions from their national parties and party leaders. Graves received a total of $35,000 from former House Majority Leader Tom DeLay's ARMPAC . Grave's Democratic opponents have criticized him for this connection . Republicans say that the charges against DeLay are politically motivated because prosecutor Ronnie Earle has a history of unsuccessful indictments against political enemies of both parties such as Kay Bailey Hutchison (R-TX), and because it has been widely reported that Earle had to shop the charges to multiple grand juries because one refused to indict.

Congressman Graves is the brother of Todd Graves, currently U.S. Attorney for the Western District of Missouri. Prior to being appointed to his post as U.S. Attorney by President Bush, Todd Graves was the Republican candidate for State Treasurer in 2000. Prior to that, Todd served as the prosecuting attorney of Platte County, Missouri.