Father Francis Davidson is accused of covering up child abuse during his time at Fort Augustus Abbey School in the Highlands.
He was accused of failing to alert police to at least one allegation.
He is quitting as monastic superior of St Benet's Hall, responsible at the Oxford college for the welfare of student monks.
His resignation comes after allegations of abuse at the now closed school and feeder school Carlekemp in East Lothian spanning 30 years. Some 50 former pupils have come forward alleging abuse at the schools between the 1950s and 1990s.
And some 10 monks have been accused of physical abuse; four monks and one lay teacher of sexual abuse including rape; and three headmasters of cover-ups.
Fr Davidson, the only surviving headmaster, gave a statement in relation to the allegations saying he had stepped down from his role at Oxford University.
He said: "Once again, I would like to offer my profound sympathies to former pupils and their families for any historic abuse.
"I was shocked and saddened to hear the allegations and of those against Bill Owen relating to Fort Augustus in the 1970s. I do not recall them being reported to me during my time as headmaster."
The NSPCC is calling for a full independent inquiry into the abuse at the school.
Fr Duggan died in 2004, but some abuse claims relate to men who are still alive.