The 44-year-old was best known for playing Samuel "Screech" Powers in the popular 1990s US sitcom about a group of high school friends and their headmaster.
He had recently completed a first round of chemotherapy after being diagnosed with lung cancer last month.
His condition had deteriorated fast in the last week, said agent Roger Paul.
"Dustin did not suffer. He did not have to lie submerged in pain. For that, we are grateful," he said on Monday.
Saved by the Bell ran for four seasons from 1989 to 1993 and was a global hit series.
Co-stars have been paying tribute.
Mario Lopez, known to fans of the show as AC Slater, said: "Dustin, you will be missed my man. The fragility of this life is something never to be taken for granted. Prayers for your family will continue on."
Mark-Paul Gosselaar, who played Zack Morris, tweeted that Diamond was "a true comedic genius" and said he "will miss those raw, brilliant sparks that only he was able to produce".
Diamond reprised his role in follow-up series Saved by the Bell: The New Class, and Saved by the Bell: The College Years. But he did not appear in the recent revival series.
The American was also a contestant on Celebrity Big Brother in 2013.
Diamond served three months in jail after he stabbed a man during an altercation at a bar in Wisconsin in 2014.