The cardinal said he sent Baker to a residential center in New Mexico for treatment and later placed him on restricted ministry.
The testimony is the first time Mahony gave a sworn deposition about how he handled allegations against Baker over a 14-year period as head of the Los Angeles archdiocese.
John Manly, the plaintiff's attorney who took the deposition in January, dismissed the cardinal's statements.
"This may be the one and only time he sits (for a deposition), and it paints a picture of somebody who obfuscates, dodges, lies and explains away everything," Manly said. "Any right-thinking person would not have engaged in the conduct Roger Mahony engaged in with Michael Baker unless they were trying to cover it up."
Baker is currently serving a 10-year sentence for child molestation.
A federal grand jury is investigating the archdiocese's handling of the clergy abuse crisis.
Six years ago, the archdiocese released a report acknowledging Mahony made mistakes in handling Baker.
"I believed too readily in Baker's contrition, and in our ability to treat and monitor him effectively," Mahony said in a statement Tuesday. "The past has informed the present, however, and I have made sure that our sexual abuse prevention policies and procedures will keep our children and young people safe from predators like Michael Baker."
The district has never located the two victims.
The archdiocese settled more than 500 cases of clergy sex abuse for a ground-breaking $660 million in 2007.
Mahony is expected to retire next year when he turns 75.