Jack Sampson, a University of Texas professor, testified in San Angelo that Jeffs, 55, was not married "under any stretch of the imagination" to the girls, ages 12 and 15.
Judge Barbara Walther ordered a recess after Jeffs, who has fired his lawyers and is representing himself, repeatedly objected to testimony from a Texas Ranger who was reading statements from Jeffs on his ranch property, The Salt Lake Tribune of Utah reported.
"The court is allowing open use of the Lord's name for religious deceit," Jeffs shouted before Walther halted proceedings and sent the jury out.
On Monday, prosecutors submitted a photograph of a girl, then 15, holding a baby in her arms that a DNA expert said Jeffs had fathered. Other photos of Jeffs with the girls were also entered.
Later Tuesday, prosecutors were expected to play an audio recording they say features Jeffs having sex with the 12-year-old.