In an interview on CBS' "Face the Nation" Graham said the Republican Party is in the midst of a "civil war" and called Trump's foreign policy positions dangerous.
He pointed to former House Speaker John Boehner's comments about his friendly relationship with Trump, and Boehner's dismissal of Texas Sen. Ted Cruz, Trump's chief Republican presidential rival, as "Lucifer in the flesh."
"There's a civil war going on in the Republican Party, obviously," Graham said. "John and I are very close friends, but he's embracing Donald Trump, and I am not. Why? Because I believe Donald Trump's foreign policy is isolationism. It will lead to another 9/11."
Graham, a one-time GOP primary rival of Trump, continued: "Let me just tell my friends, who I really do respect, if you are embracing Donald Trump, you're destroying conservatism. You will make it hard for this party to ever regain footing with Hispanics, because his immigration proposal is unworkable, is hateful. When it comes to women, we're alienating women, who should be coming our way after eight years of Obama."
He also invoked Boehner's comparison of Cruz to Lucifer.
"There's been a lot of talk about Lucifer," Graham said. "I think Lucifer may be the only person Trump could beat in a general election. But when it comes women and Hispanics, Trump polls like Lucifer."
And he said he'd like to see Cruz continue his campaign even if he loses Indiana's crucial primary on Tuesday, where 57 delegates are on the line -- along with the mathematical likelihood that anti-Trump Republicans can stop the real estate mogul's march to the GOP nomination.
"I'm advising Ted, go to the last vote," Graham said. "Trump's gotten 40% of the popular vote. That doesn't give you 1,237 delegates. I think you could still stop, even if you lose in Indiana."
Trump responded with a critical tweet, asking: "Why don't they say that I ran him out of the race like a little boy, and in the end he had no support?"
An NBC/Wall Street Journal/Marist poll out Sunday showed Trump with a commanding lead in Indiana, at 49% support to Cruz's 34% and Ohio Gov. John Kasich's 13%.
Conservative blogger and pundit Erick Erickson tweeted comments similar to Graham's. He said: "If the WSJ poll in Indiana is accurate, not only is the primary process over, the GOP is too."
Erickson then followed up: "True, the GOP will actually survive, but it's going to be a brutal two years. The state parties will be the saving grace of the GOP."