RIYADH, Saudi Arabia—Months after the start of an anticorruption crackdown, Saudi authorities are still holding a senior prince and several dozen businessmen and former officials in detention and recently have made new arrests, government officials said.

Some of the detainees have been beaten and deprived of sleep while being questioned, officials and people close to the detainees said. In some cases, these people said, those in custody haven’t been charged with crimes and have been permitted little or no contact with relatives...