Dr Biden told CNN that Mr Graham's comments about her family have been "hurtful", and that she and her husband were once "great friends" with the South Carolina politician.
Whereas they once travelled together and dined together, things have changed.
"Now, he's changed," Dr Biden said. "I don't know what happened to Lindsey... It's hard when you consider somebody a friend and then they've said so many negative things. That's been a little hurtful."
The comments come after repeated attacks by Republicans during the impeachment effort, who have urged the Senate to bring forward Hunter Biden as a witness. Mr Trump has found himself facing the impeachment trial in part because of his efforts to coerce the Ukrainian government into investigating the former vice president and his son, who was given a seat on the board of a Ukrainian energy company while his dad was in charge of Ukraine policy.
"Hunter has done nothing wrong," Dr Biden laughed when asked about efforts to compel him to testify. "Why would Hunter be called? Donald Trump should be before that committee."
Mr Graham has evolved into an ardent supporter of Mr Trump's, after once being a vocal critic of the man during the 2016 election.
The president's rise to power has been marked by even deeper partisan divides in Washington, with many Republicans and Democrats seeing the damage done as potentially irreversible.
Mr Biden, for his part, has maintained a belief that he could unite Republicans and Democrats should he become president, in spite of criticism that nothing like that was seen during the Barack Obama presidency, and in spite of his apparent falling out with a once close Republican friend, Mr Graham.
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