The wrenching process of putting its money where its mouth is and cutting programs to keep its balanced budget commitment for fiscal 1981 is under way in Congress.

Two of the first targets showed up yesterday, as a House committee moved toward cutting back the federal child nutrition programs and a Senate panel voted to give federal retirees only one cost-of-living increase in their pensions each year instead of two.

More of the painful belt-tightening will occur this week and next, as committees face deadlines for coming up with cuts to meet the terms of the balanced-budget resolution adopted earlier this month.

The Senate Budget Committee, using recommendations in memo form from authorizing committees, is scheduled to meet today to work on a final package that adjusts spending to the resolution. Similar House action is set for next week.

In the legislative lexicon the term for this is "reconciliation" -- that is, reconciling spending on existing programs with spending targets in the resolution.

It is painful process. It means slashing programs for constituents that the committees already have deemed vital and inviolate.

The Senate Governmental Affairs Committee, in an example of this, after two tie votes narrowly decided to make cost-of-living increases for federal pensioners annual instead of semi-annual.

Such a step would save $553 million in fiscal 1981, allowing the committee to meet its target. The deciding ballot in an 8-to-7 vote was cast By Sen. Carl Levin (D-Mich.), who strolled in at the last moment.

A House Education and Labor subcommittee's recommendation that $500 million be chopped from child feeding programs will come before the full committee today -- and there, the pain is enormous.

Chairman Carl Perkins (D-Ky.), generally viewed as the patron saint of school-lunch programs, found himself in the agonizing position of recommending the reductions to his panel.

Meanwhile yesterday, on the other side of the pain gauge, the Senate Finance Committee hammered out a program of tax adjustments that would raise $4.2 billion in a new federal revenues for fiscal 1981.

Demonstrating its distaste for that sort of election-year castor oil, the committee agreed that $3.1 billion of the total package would be raised on a 1981-only basis.

Among its moves, the committee decided to tax capital gains for foreigners who sell real estate in the United States, to leave the 2 percent federal excise tax on telephone bills intact, and to tax an employer's payment of his employes' payroll taxes.

Also approved were three Carter administration cash-management proposals, altering the ways in which estimated income is taxed, which would raise $3.6 billion next year.

On the House side, the Ways and Means Committee, voting 17 to 16, beat back an attempt by liberals and organized labor to reverse an earlier-approved reduction of $800 million in the trade adjustment aid program that compensates workers and companies injured by foreign competition.

The House Post Office and Civil Service Committee will continue its efforts today to find a way of reducing its spending authorization by $1 billion.

About half of the reduction may come from altering federal retirees' inflation allowances; the other half, by ending Saturday mail deliveries. But in two days of haggling, the committee has reached no decisions.

"No one looks at the impact of all these cuts called for in the budget resolution," said a committee aide. "It is very painful. Why cut the retirees? Why Cut Saturday mail? Hell, why not close down the Department of Housing and Urban Development?"