Green sent a letter on Thursday, calling Field’s allegations during a radio interview last week “disgraceful.”
They will be replaced by David Hägglund who has been named sole creative director of both brands.
The appointment comes as Sir Philip Green shakes up the management ranks at Arcadia and its parent Taveta.
Taveta is the parent of Green’s Arcadia retail group, which comprises fashion brands Topshop and Topman.
Samuel, Donald Newhouse are reported to have a joint fortune of $27.06 billion.
Pinaults, Greens and Santo Domingos are in top five.
Staff voted to strike over a dispute concerning their hourly wage.
The regulatory body had launched an investigation into BHS in March.
Parliamentarians approved without a vote and supported a nonbinding motion without opposition.
Taveta Investments hires lawyers to scrutinize parliamentary report.
BBC’s Panorama program reveals bonuses made to top BHS staff.
Al Mana bought BHS brand and international franchise business following the retailer’s collapse.
Green issued a statement in response to press, parliamentary comments.