The President's Private Sector Survey on Cost Control yesterday agreed to send President Reagan 561 recommendations it says it hopes will cut government spending by as much as $57 billion over three years.

Including cuts of more than $38 billion in federal employes' benefits and $7 billion in food stamps, the recommendations were contained in six task force reports issued last week. They were approved unanimously by voice vote of a 34-member subcommittee empowered to act for the full panel.

The private-sector survey, a group of 163 businessmen headed by industrialist J. Peter Grace, was established by Reagan last June and charged with finding ways to save federal money through better management.

But some of its recommendations already have run into opposition from several advocacy groups, which say the panel is trying to influence policy, and from Rep. William D. Ford (D-Mich.), who said that the study of federal employe benefits was inaccurate and amounted to "statistical chicanery."

"What's chicanery?" asked Grace. He called Ford's charge a "vitriolic attack," and accused the congressman of "engaging in a numbers game."

The director of the personnel task force, management consultant Sy Pranger, conceded that the group had "compared apples and oranges" in its analysis of public benefits versus private benefits, but he said the figures had been adjusted to minimize their dissimilarities.

The panel did not hear public testimony yesterday, but written comments were little better received than Ford's complaints.

Responding to a letter from the National Anti-Hunger Coalition, an amalgam of public-interest groups that criticized the food-stamp cuts, Grace said, "What do they want to do? Stop it or what?"

Grace also dismissed a letter that found fault with a recommendation that the federal government recoup its full investment in electric power marketing associations, saying that the criticism had come from people who stood to lose money if the recommendation were adopted.

Panel members asked few questions about the recommendations, and suggested only two minor changes. For example, potential savings of $212 million were changed to "partly substantiated" rather than "fully substantiated" after one panel member found the number "indefensible." The panel also deleted the report's characterization of the Health and Human Services Department as "an organization dedicated to self-preservation."

The six reports approved yesterday involved four departments, five executive agencies and the federal work force. They are the first of 38 such task force reports that are to be released this month and next. The next group of reports is scheduled for release Monday.