Oakman's departure comes after HW reported that the St Albans garden has had difficulties with staff retention following its £500,000 re-opening in June (HW, 22 November).
It is now employing contractors, who new chief executive Roz Hamilton would not name but said were rose experts.
Hamilton, originally slated for a general manager role, was made chief executive by the board to succeed Richard Adams at an emergency meeting last week.
She said: "Neil was not a rose expert. It's no secret three gardeners have left. None were rose experts. There is an argument that that's a shortfall on us as a society. It is a specialist area and not something that can be learnt overnight. We have to have appropriate staff.
"That's where a lot of the disagreements have come from."
Hamilton said the contractors were "on top of what needs to be done". She added that she comes "from a commercial background and has a strong passion for roses".
Oakman, who could not be contacted, is believed to be leaving the area.
- See p10 for more RNRS news.