This is the first day of a civil defamation case in which a federal judge has already determined the former New York mayor and Trump lawyer is liable for defaming Wandrea "Shaye" Moss, a voter registration officer, and her mother Ruby Freeman, who was a temporary worker for the election.
The jury could order Giuliani to pay millions of dollars in damages.
Moss and Freeman accused Giuliani of orchestrating a "sustained smear campaign" by falsely accusing them of election fraud as Giuliani searched for evidence to bolster Trump's effort to overturn his election loss to Democrat Joe Biden.
The pair are expected to testify at the trial, which is due to conclude this week.
Von DuBose, a lawyer for the two women, told jurors in his opening statement on Monday that Giuliani and other Trump allies "stole the lives of Freeman and Moss by destroying their names".
DuBose played a sampling of recorded messages Freeman and Moss received after the election that were filled with racist and sexist slurs and accusations the pair had committed "treason".
The lawyers said they would seek tens of millions of dollars in damages at the end of the trial.
Giuliani, who sat in the courtroom during opening arguments, also may take the witness stand.
His lawyer, Joseph Sibley, conceded Giuliani "did something wrong" but said the attacks on Freeman and Moss "involved a lot of people."
"You're going to see a lot of evidence of harm, but not much evidence that Mr Giuliani was the cause," Sibley told the jury in his opening statement.
If the jury awards Freeman and Moss what they are seeking, Sibley said, it "will be the end of Mr Giuliani."
According to court documents, Giuliani referenced surveillance footage he falsely claimed showed the workers hiding "suitcases" full of illegal ballots under tables at a vote processing centre in Atlanta, and counting ballots multiple times.
He accused them of surreptitiously passing around a USB drive. The purported computer drive was actually a ginger mint, the two later said.
A state investigation found the two were properly and legally counting votes.
Moss and Freeman, who are Black, alleged they were subjected to a torrent of racist abuse and violent threats.
US District Judge Beryl Howell, who is overseeing the case, has already found Moss and Freeman are entitled to damages on their claims of defamation, infliction of emotional distress and conspiracy.
The judge ruled in August that Giuliani had made it difficult for them to prove their case at trial by failing to turn over evidence as required.
The jury's verdict could worsen financial problems for Giuliani, who has faced a series of legal and professional woes for his work for Trump after the election.
Giuliani was indicted in August in a sweeping racketeering case in Georgia against Trump and several of his allies, in part for his alleged targeting of Freeman and Moss. Giuliani has pleaded not guilty.
Moss and Freeman settled defamation claims with the far-right One America News Network for an undisclosed sum last year.
