It was the latest legal challenge to the settlement filed by the London-based oil major, which has complained previously that Juneau has been too generous and liberal when approving claims.
Juneau has said he is just applying the rules of the settlement agreement.
BP originally expected the March 2012 class-action settlement to resolve economic and health claims by more than 100,000 individuals and businesses to cost $7.8 billion.
It has since said the uncapped program could cost $9.2 billion and that this amount could grow.
The filing in US District Court in New Orleans said Juneau lacks neutrality because he had advocated for claimants before the court appointed him to run the claims program.