The Senate began its long-delayed debate over the Supreme Court nomination of Judge Robert H. Bork yesterday with a clash over the process that has brought Bork to the verge of almost certain rejection.

With Bork's wife, Mary Ellen, and his son, Robert Jr., watching from the visitors' gallery, Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) opened the debate by describing Bork's views as a threat to "the traditional core of our national character and our constitutional history."

Biden said charges that Bork was the victim of "lynch mobs" were "nothing but a smokescreen to distract the Senate and the American people" from Bork's testimony before the Judiciary Committee.

It quickly became evident, however, that Bork's supporters intend to use the Senate floor debate in an attempt to discredit the confirmation process, particularly the campaign waged by liberal groups against the nomination.

Sen. Orrin G. Hatch (R-Utah), one of Bork's most outspoken defenders, said Bork had been victimized by "a dirty tricks political campaign." Holding copies of full-page newspaper advertisements by People for the American Way and the National Abortion Rights Action League, Hatch said the two anti-Bork messages contained a total of 151 "falsehoods, slants and distortions."

He described a television commercial against the Bork nomination narrated by actor Gregory Peck as "absolutely false, filled with innuendo, outright lies."

The debate was only an hour old when Hatch and Sen. J. James Exon (D-Neb.) began squabbling over who would be recognized next on the floor. Hatch later clashed with Biden, who challenged him to read the portions of the Judiciary Committee report on the Bork hearings that he had described earlier as "distortions."

The initial tone suggested that the debate may be a bitter replay of the charges and countercharges made by both Bork's critics and his defenders in the weeks before the committee hearings. There was also no indication of how long the debate will last.

With 54 senators publicly committed to vote against confirmation, Senate Majority Leader Robert C. Byrd (D-W.Va.) called for the debate to end before the end of the week. But Byrd's attempts to reach an agreement with Senate Republicans for a deadline for the vote have so far failed because of objections to a time limit by a handful of Bork's conservative supporters.

Anticipating the assault on the confirmation process, Bork's critics charged yesterday that President Reagan was motivated by political considerations in nominating the controversial Bork to succeed retired justice Lewis F. Powell Jr.

"Any politicalization has been driven by President Reagan's single-minded pursuit of a judiciary packed with his ideological allies," Biden said. He added that Reagan "nominated Judge Bork to pursue an agenda that has been repudiated by Congress."

"In choosing Robert Bork, President Reagan selected a nominee who is unique in his fulminating opposition to fundamental constitutional principles as they are broadly understood in our society," Sen. Edward M. Kennedy (D-Mass.) said.

Asserting that Bork "has made a career out of opposing simple justice," Kennedy said it was "preposterous and hypocritical" for Bork's defenders to complain about the confirmation process.

"Judge Bork himself was a far greater threat to the role of the Supreme Court than anything that happened in this debate," he said. "His nomination collided with the Constitution and with democracy in America, and the Supreme Court and the country have emerged the stronger for it."

Bork's wife and son left the visitors' gallery as soon as Kennedy, one of Bork's harshest critics, rose to speak. They returned to the gallery after Kennedy finished.

Biden defended the Judiciary Committee hearings and said that Bork faced defeat largely because his judicial philosophy put him "at odds with the great tradition of {recognizing} unenumerated individual rights" in the Constitution.