President Reagan's budget-cutters are proposing slashes of about $700 million beyond those-already disclosed for federal school lunch and food programs for the poor.

The bulk of the new cuts, targeted after a second round of review of the Department of Agriculture budget in recent days, would affect school children and people who live in Puerto Rico.

Proposed cuts in federal feeding programs now are in the neighborhood of $4.2 billion, about one-tenth of the overall budget slashes Reagan will seek.

According to sources, the president's fiscal 1982 budget proposals, scheduled for release this week, will call for these additional reductions:

The elimination of a summer free lunch and breakfast program that feeds about 2.1 million mostly poor school children at a cost of $122 million.

A cut of about $300 million in feeding assistance to Puerto Rico, where 58 percent of the island's 3.2 million residents now receive food stamps. Under the Reagan plan, the reduced aid would be consolidated into a block grant and turned over to commonwealth authorities for distribution.

A cut of about $90 million, from around $120 million down to $30 million, from a special milk subsidy to school-lunch programs, a reduction similar to that proposed without success by the last four administrations.

An additional $20 million reduction on top of the roughly $300 million cutback already scheduled for a politically popular supplemental food program for about 2.2 million women, infants and children (WIC).

An extra fillip in the new budget proposals, demonstrating the political sensitivity of the cuts, shows restoration of $20 million that had been sought by conervative Rep. John M. Ashbrook (R-Ohio) for feeding programs in privately owned child-care centers.

The food-program cuts disclosed earlier, about $1.8 billion in food stamps, $1.7 billion in child nutrition and the $300 million from WIC, drew a sharp and bitter reaction from child-care, labor and social-welfare organizations.

The new reductions are likely to run into a similar buzzsaw Tuesday, when a House Education and Labor subcommittee is to meet to discuss the administration's assualt on child-nutrition programs.

Among others, Ashbrook and Rep. William F. Goodling (R-Pa.), are expected to raise challenges to Reagan's plans for the school-feeding programs. Goodling is preparing a bill aimed at preserving the school lunch setup with only minor changes.

Republicans and Democrats were united last year on school lunches. There is a concern that proposed changes to drop higher-income children could destroy the lunch program, and you will see some Republicans disassociating themselves from the administration proposals," a committee aide said.

The proposed cuts for the Commonwealth of Puerto Rico, however, may be another story. Although they are U.S. citizens, Puerto Ricans hav little political leverage. They do not pay federal income taxes and they cannot vote in presidential elections.

An aide to Baltasar Corrada, Puerto Rico's nonvoting delegate in the House, said, "We are realists, but we would fight any cuts that fall outside of a framework of weeding out fraud and mismanagement."

At current levels, the various federal nutrition programs cost around $1.2 billion in Puerto Rico, with roughly 80 percent of that in food stamps.

Reagan's proposals for Puerto Rico mean that his overall food stamp reduction plan will be closer to $2 billion than the $1.8 billion already envisioned, sources indicated.

The proposal to combine nutrition aid for the island into a single block grant, food-stamp experts said, could create "administrative chaos," because the Department of Agriculture has acknowledged that serious food-stamp management problems exist there.

The summer feeding program on the mainland, also acknowledged to have administrative problems, is essentially a continuation of regular school-year lunches and breakfasts for more than 2 million poor children.

The Carter administration had proposed that it be budgeted for $136 million in fiscal 1982, up $14 million from the current $122 million. The program's severest critics have included Sen. Jesse A. Helms (R-N.C.), now chairman of the Senate Agriculture Committee, which will deal with proposed changes in the feeding program.

Helms, however, and other conservative legislators have supported the WIC program, which provides milk, cheese, eggs, infant formula, juice and other supplements to poor pregnant women and young children.

Recent studies have demonstrated positive effects from WIC: higher birth weight, less infant mortality, reduced hospitalization costs and accelerated child growth rates.