Republican South Carolina Sen. Lindsey Graham launched his harshest attack against his 2016 presidential rival Donald Trump on Tuesday, calling the businessman a "complete idiot," and promising to "beat his brains out" if the two were to face off in the Republican primary in Graham's home state.

"Come to South Carolina, and I'll beat his brains out," said Graham during an interview on CNN Tuesday, despite the fact that he has gained little to no traction in national polls.

Graham also described voters who back the GOP frontrunner as a frustrated group of people that also falsely believe President Barack Obama is a Muslim who was born in Kenya.

"There's 30 percent of my primary electorate that believes that Obama's a Muslim, that he's born in Kenya, and that would deport everybody," Graham said. "So there's a dark side of politics that Mr. Trump's appealing to."

Graham also called the billionaire real estate mogul's immigration reform proposal demagoguery.

"Demagoguing immigrants -- he's not the first guy to do this, and he won't be the last, and there's always a market for it, but it's not sustainable," said the senator.

Graham's attack came after Trump mocked the senator earlier in the day by highlighting a poll of South Carolina GOP primary voters which reveals that he is a head of the all GOP candidates with 30 percent, while Graham has garnered only 4 percent.

"Congrats," Trump tweeted at Graham, adding that those four percentage points are "far better than zero nationally."

In response, Graham also called Trump a "showman" whose "policy positions are complete gibberish."

"He is shallow, he is ill-prepared to be commander-in-chief, he doesn't know what he is talking about in terms of how our laws work, he says the worst things possible about immigrants and women, and he's a complete idiot when it comes to Mideast policy," Graham said. "So I think over time, common sense will prevail."