Mr Higbie served as a surrogate for Mr Trump's campaign in 2016 and has worked as a spokesman for the Great America PAC, which supports Mr Trump.
After CNN re-posted the clips, which were taken from from a radio show Mr Higbie formerly hosted called "Sound of Freedom", he resigned.
A spokeswoman for CNCS, a federal government agency that runs a number of volunteering programmes working to alleviate social problems such as poverty, said the resignation was "effective immediately".
During the internet talk show, which the conservative commentator ran from 2013 and 2014, he expressed a dislike of Muslims, black people and homosexuality.
"I just don't like Muslim people. People always rip me a new one for that. 'Carl, you're racist, you can't, you're sexist.' I'm like, Jesus Christ, I just don't like Muslim people because their ideology sucks," he says in one excerpt, describing Islam as "the ideology of a child molester".
In another, he tells Muslims: "Go back to your Muslim s***hole and go crap in your hands and bang little boys on Thursday nights."
The clips have surfaced after Mr Trump was accused by Democratic Senator Dick Durbin of repeatedly using the word "s***hole" when speaking about African countries during a meeting about immigration last week.
The remarks were condemned by leaders around the world and branded "racist" by the UN.
Mr Trump has denied he is a racist, telling a reporter on Sunday: "I'm the least racist person you have ever interviewed."
Neither Mr Higbie nor the White House were immediately available for comment.
The original article was published in the Independent.
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