The pup's owner, Eric Sauma, tells TMZ ... the Boston Terrier passed away over the weekend, going peacefully in his sleep. Eric's parents went to go wake Swatch up for breakfast, but he already crossed the rainbow bridge.

We're told he made it to the end of his breed's lifespan, dying at 15 & a half years old -- slightly older for his breed.

Eric says the last few months were rough for Swatch ... his hips were starting to go, and he became blind by the end.

Fans of the show remember Swatch as a furry icon, serving as the mascot of Mood Fabrics, where the designers on the series get their intricate needs met. The terrier would often greet the contestants, or just take a snooze during times of intense panic.

The show's currently taping its 20th season, and Eric says his team is working on a memorial ... noting there are discussions about highlighting him on the show, but that's still TBD.

He tells us they're going to cremate Swatch and build a shrine at Mood Fabrics HQ in New York City, where fans can visit him.