The board of the hospital accepted Bettschart’s resignation on Monday, the hospital said in a news release.
The hospital did not say when precisely he will leave other than to say it will be within the legally prescribed period.
Controversy about the surgeon erupted in 2010 when he was accused of watching football matches on TV during operations, the ATS news agency reported.
Further shock waves hit when Vigousse, a satirical journal, disclosed two suspect deaths at the hospital.
Bettschart has been cleared of wrongdoing by an internal investigation but he faces a criminal complaint laid by the family of one of the victims and a parliamentary investigation, ATS said.
The hospital, however, praised the surgeon for his work, saying the level of surgery improved there thanks to the work of him and his team.
The Valais hospital is one of the rare hospitals in Switzerland not attached to a university that practises highly specialized visceral surgery on the liver, the rectum, the pancreas and the esophagus.