Rep. Parren J. Mitchell (D.-Md.) yesterday urged the nation's black businesses to serve notice on the Carter Administration that "no man slaps the face of the black community with impunity."

Mitchell, an ardent advocate of black rights, singled out Commerce Secretary Philip M. Klutznick as "too callous and insensitive" to the plight of blacks. Mitchell's remarks before a minority business group meeting here were in response to statements Klutznick made before the group on Thursday and during a press conference later that day. In response to reporters' questions, Klutznick said that black businesses aren't facing an emergency situation during the recession.

Mitchell also said he wants to see the Carter administration's plan for helping blacks during the 1980s and that he hopes this plan consists of more than the "feeble effort by the administration" to establish the Minority Business Development Administration.

A bill to grant legislative authority to the MBDA within the Commerce Department is pending on Capital Hill. The MBDA was formerly the Office of Minority Business Enterprise and was established through an executive order.

Mitchell called the legislation a "pieback plan." He explained that the back of a pie has no spine and that the MBDA legislation also has "no dentures, no teeth, no hands . . ." The end of the remark was drowned in applause.

Klutznick had addressed the same black group, the Chicago Economic Development Corp. on Thursday and said that minority groups -- blacks in particular -- still bear a disproportionate share of the hardship that accompanies inflation and recession.

During a press conference following his address Klutznick was asked by reporters about a new 11-point emergency plan that Mitchell and 35 black business owners had presented to Vice President Walter Mondale and House Speaker Thomas P. O'Neill Jr. (D.Mass.) to help minority businesses during the recession. Kluntznick said that an emergency plan isn't needed but that when an emergency situation does arise, "We'll need emergency funds." b

Following Mitchell's speech, a Commerce Department spokesman called the Washington Post and said that Klutznick had misunderstood what plan the reporters were talking about. The spokesman also said that Klutznick had called Mitchell following the congressman's speech and that they had agreed to discuss their differences soon.

In a telephone interview later, Mitchell said that he had agreed to meet Klutznick but that they had had "no substantive discussion" over the telephone.

Mitchell said during his speech that he was upset but not surprised about Klutznick's remarks.

"It's a fairly typical response," Mitchell said. "It's the kind of response I hear every day in the government and in the private sector from those who've abandoned black people . . ." He said Klutznick's remarks were typical of those "who have never given a tinker's damn" about blacks.

Before Mitchell's speech, the Rev. Jesse L. Jackson said that blacks must depend on themselves and not on the government to get ahead economically, and possibly should begin using economic boycotts.