Mr Biden, who has carried a speech impediment throughout his life, was discussing those individuals who have reached out and asked him for help over the course of his political career.
“My wife and I have a call list of somewhere between 20 and 100 people,” he said towards the end of the debate. “I give them my personal phone number.” The former vice-president then described how a “little kid” with a stutter had once asked him: “I, I, I, I, I can’t talk. What do I do?’”
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Failing to spot Mr Biden’s reference to his own personal experiences, Ms Sanders tweeted: “I I I I I I I I I I I I I I I hhhave (sic) absolutely no idea what Biden is talking about. #DemDebate”
Mr Biden, who last month opened up on his speech impediment in an interview with the Atlantic, replied on Twitter: “I’ve worked my whole life to overcome a stutter. And it’s my great honor to mentor kids who have experienced the same. It’s called empathy. Look it up.”
Ms Sanders attracted fierce criticism for her comments before insisting she was “not trying to make fun of anyone with a speech impediment. Simply pointing out I can’t follow much of anything Biden is talking about.”
The ex-White House official, who left her role as press secretary in July, later deleted her original tweet and issued a second apology: “I actually didn’t know that about you and that is commendable. I apologize and should have made my point respectfully.”
During a Democratic presidential debate in July in Detroit, questions were raised of Mr Biden’s health after he appeared to stutter during a discussion on health care.
The 77-year-old addressed the moment in his interview with the Atlantic while admitting his boyhood stutter used to be a source of “shame” for him. He also revealed how he had been left with “anger, rage, humiliation” after once being mocked by a schoolteacher.
Earlier this year, Mr Biden was filmed in Keene, New Hampshire telling a young person with a stutter that “it does not define you, it cannot define you”.