Members of the Maricopa County Board of Supervisors spoke with disgust at times about County Assessor Paul Petersen during a meeting in Phoenix.
Content recovered on the laptop and noted in a report to the board included text messages of pregnant women being threatened when they changed their minds about giving up their newborns.
"To say this is disturbing to all of us on the board is certainly an understatement," said Bill Gates, board chairman.
The panel unanimously voted to ask the county attorney to start the process to remove Petersen based on willful misconduct. The Republican was arrested and charged in a scheme involving the adoption of babies from the Marshall Islands.
Petersen has pleaded not guilty in Arizona, Arkansas and Utah to charges involving the adoption of babies from the Marshall Islands through his law firm.
Prosecutors say he illegally paid women up to $40,000 to have their babies in the United States and give them up for adoption. Charges include human smuggling, sale of a child and fraud.