The Al-Hasawi family have seen fit to remove the three from the positions of club executive, club ambassador and head of recruitment in a boardroom overhaul
Arthur had been club executive for 13 years, Burt was head of recruitment for seven years and Clark is a club favourite and had many roles, with his most recent club ambassador.
A source close to Clark, a former European Cup winner, said the sacking came "out of the blue".
The 69-year-old had spent four years as a player at the City Ground, before coming back to replace Brian Clough as manager in 1993.
Their sackings have come at the hand of the club's Kuwaiti owners, the Al Hasawi family.
Elsewhere at the City Ground, manager Alex McLeish has confirmed that Karl Darlow will be the club's new first-choice goalkeeper, replacing Lee Camp, who is set to leave Forest after failing to agree a new deal.
Darlow has just returned from a loan spell at Walsall and has only ever played three times for the Reds but will play ahead of newly-arrived Kuwait international Khalid Al-Rashidi.
McLeish told BBC Sport: "The only goalkeeper that will be coming in is Khalid. He'll be back-up to Darlow until he acclimatises."