The chairman of Avon Corp., David W. Mitchell, yesterday announced he was resigning from the board of J.P. Stevens & Co. to remove his company from a union pressure campaign to organize Stevens, a textile manufacturer.

Mitchell, along with J.P. Stevens Chairman James D. Finley, resigned from the board of Manufacturers Hanover Corp. on March 7 after the Amalgamated Clothing and Textile Workers Union had directed its unusual corporate campaign at the bank and had gotten several other unions to withdraw pension funds from management by Manufacturers Hanover in protest.

The union has been trying to organize J.P. Stevens since 1960 and, until recently, has gotten nowhere in what is an increasingly bitter battle. Now, however, the union feels its campaign to isolate J.P. Stevens board members and affect their other corporate interests in beginning to succeed.

"This is the beginning of the alienation of the Wall Street community from J.P. Stevens," commented Ray Rogers, director of the union's corporate campaign.

In a statement, Mitchell attributed his departure from the Stevens board directly to the union (unlike the decision to leave the Manufacturers Hanover board, which he claimed was due to "business-time conflicts").

"Despite my desire to continue to assist Stevens' management, for whom I have the highest regard in its controversy with the Amalgamated Clothing and Textile Workers Union, I cannot permit Avon to be drawn into the conflict and to be subjected to the pressures which the union is exerting as a result of my Stevens board membership," Mitchell said.

But Rogers indicated that Avon is not yet off the hook, because another Avon director, Ralph Manning Brown Jr., who also is chairman and chief executive officer of New York Life Insurance Co., sits on the board of J.P. Stevens.

Rogers said that Brown was "going to have to make a decision to stay with Avon or with J.P. Stevens" as an outside director. He noted that his union now also is aiming its fire at another Stevens director, the chairman of the Seamen's Bank for Savings, E. Virgil Conway, who also is a director of Consolidated Edison, the New York City utility.

Through a New York Life spokesman, Brown said he had no plans to resign from the Stevens board because he thought he could be "of greater service sitting on the board as an outside director" than by departing. "The spokesman also said Brown intended to stay on the Avon board.

A spokesman for Avon, where Brown has been a director for 14 years, said he "can remain on our board as long as he desires."

"David Mitchell has been a very fine and active director of our company and we regret that he finds it necessary to resign," Stevens Chairman James D. Finley said a brief statement.

After his resignation from the Manufacturers Hanover board, Finley said that, because of the union campaign, "The bank put enough pressure on me that I decided against seeking re-election . . . I don't want to be where I'm not wanted."

The AFL-CIO recently designated Stevens the 'No. 1 laborlaw outlaw," based on what it considers a protracted series of labor law violations and unfair practices.

The Amalgamated Clothing Union won a representation election at a large Stevens' textile complex in Roanoake Rapids, N.C., in 1974, but no contract has yet been signed. A National Labor Relations Board administrative law judge ruled last December that Stevens had bargained in bad faith at Roanoke Rapids "and without any intention of concluding a collective bargaining agreement."