The spat between Bernie Sanders and the chief executive of General Electric is getting personal.

"If the CEO of General Electric (GE) wants to know how his company is destroying the fabric of America, he should take a good look in the mirror," Warren Gunnels, policy director for the Sanders campaign, told CNN on Thursday.

The Sanders team criticized GE CEO Jeff Immelt over his retirement package, which it claimed was worth tens of millions of dollars, and for being a leader of "a business group lobbying Congress to slash Social Security, Medicare, and Medicaid." That's likely a reference to Immelt being involved in Fix the Debt, a group pushing Congress to reduce the debt by cutting spending and raising taxes.

GE didn't immediately respond to CNNMoney's request for comment on the remarks.

Related: Bernie Sanders: JPMorgan and GE are destroying the fabric of America

This is actually Round III of the duel between Sanders and GE.

It all started with a wide-ranging interview with the New York Daily News in which Sanders said GE is "destroying the fabric of America." The full transcript of the interview came out Monday.

Immelt fired back with an entire op-ed in the Washington Post on Wednesday defending his company as creating wealth and jobs "instead of just calling for them in speeches."

He slammed Sanders for never visiting a GE aviation plant in Rutland, Vermont, even though Sanders is a U.S. senator from the state.

"We've never been a hit with socialists," Immelt wrote. "We're in the business of building real things."

Related: GE to Bernie Sanders: We've 'never been a big hit with socialists'

Sanders has said often that if he's elected president, Wall Street and big business probably won't be happy. He is running on a platform of creating a more fair and "moral economy."

For Sanders, GE and Immelt are examples of what's wrong with America. GE is abandoning the U.S. by shipping jobs overseas and not paying its fair share in taxes, he argues.

"General Electric has been throwing American workers out on the street and moving to China and other low-wage countries," the Sanders campaign said Thursday.

A CNNMoney analysis this week pointed out that 68% of GE's employees were in the U.S. in 1995. Today, the U.S. share is only 38%.

Sanders vows to make GE and large companies like it pay more in taxes.

Related: 'I love Bernie, but I don't want my taxes to go up'

His campaign also suggested that Americans may stop buying GE products as word gets out about the company shipping jobs abroad.

Sanders "will also demand that if General Electric wants Americans to continue to buy their products, they better start making more of those products in the United States, not in China or Mexico," the campaign spokesman said Thursday.

-- CNNMoney's Matt Egan contributed to this article.