Someone gained entry by kicking in the second-floor back door of the building sometime after Monday, officials said. They discovered the damage Thursday.
The intruder scratched out the word "Republican" and replaced it with an offensive slur used to describe gay people, Wayne County GOP Chairman Brent Heath said.
Nothing was stolen and only the mural was damaged, he said.
"It appears to me that their motive was to get in and deface that mural," Heath said to the News & Observer.
Officials hope to restore it. "I have talked to the lady who did it originally and she's going to see what she can do," Heath said Friday.
Other offices in North Carolina have also been damaged this year. In October, the Orange County Republican headquarters in Hillsborough was firebombed. In Alamance County, the Republican Party's building was defaced with profane graffiti before Election Day. And at the state Republican Party headquarters in Raleigh, banners celebrating Donald Trump's victory in the state were slashed.
"These are not acts of speech, they are acts of destruction and violence," Dallas Woodhouse, executive director of the North Carolina Republican Party, said in a statement. "Nothing good can possibly come from these events and they must be condemned. We continue to urge our local offices across the state to be in contact with local law enforcement to assist with protection of NC GOP volunteers and property."