In a statement, Mr Mansfield said: "I joined the campaign LAWH in order to defend the right of those who wished to voice legitimate criticisms of the government of Israel and their repeated violation of International law from being unfairly categorised as antisemitism.
" An objective shared by fellow campaigners Moshe Machover, Ken Loach and Noam Chomsky.
"Recently I have been alerted to the material being promulgated by the campaign, (not by the supporters named above).
" I was unaware of this and both the tenor and content are unacceptable. For these reasons I wish to withdraw my sponsorship of the Campaign, whilst at the same time wishing to maintain my enduring support for a responsible and vigorous critique of any government which flagrantly undermines the rule of law."
The vice-chairman of LAWH is Tony Greenstein - who used antisemitic slurs including the term "Zio". He was expelled from Labour earlier this year.
Jackie Walker, who remains suspended by Labour over allegations of antisemitism, is another member of the group.