The Senate yesterday approved sharp reductions in federal food stamps, cutting 1 million recipients from the rolls, but it rejected conservative attempts to slash the program more deeply.

The bill, tailored along the lines of President Reagan's proposal for cutting benefits, would reduce federal spending by about $1.5 billion in fiscal 1982.

The final vote of 77 to 17 found Sen. Jesse Helms (R-N.C.), chairman of the agriculture committee that crafted the measure, voting against final passage. Other opponents included Sen. Harry F. Byrd Jr. (Ind.-Va.).

The final version was as much a victory for the administration, although its approach to savings differed from that of the president, as it was a rebuff to Helms and other conservatives who sought deeper slashes in the program.

A coalition led by Sens. Robert J. Dole (R-Kan.) and Patrick J. Leahy (D-Vt.), both members of Helms' committee, successfully fended off attempts to cut the program even more severly.

Helms and his allies contended that the food stamp program, largest of the federal welfare endeavors, was still too generous and open-ended, notwithstanding his committee's major overhaul of eligibility requirements and guidelines.

The new requirements, tightening eligibility, will remove at least 1 million beneficiaries from the program and reduce benefits for virtually all of the other 22 million recipients of food assistance.

Under terms of the measure, which is similar to a version pending in the House, the program would be limited to a cost of $10.8 billion in fiscal 1982. If left unchanged, the program would have cost at least $12.3 billion, by committee estimates. Over is four-year life, the bill would cut spending by about $8 billion.

In effect, the legislation repeals a series of liberalizing steps applied to the program in recent years, but it retains several features that conservatives attacked vigorously.

In the face of the Dole-Leahy muscle, Helms dropped plans to attempt to reduce a family's stamp benefits if a child from the family receives free school lunches. An amendment by Steven D. Symms (R-Idaho), requiring recipients to pay for part of their benefits, was defeated, 66 to 33.

Major savings would be achieved in the program by tightening gross income eligibility limits in all cases to 130 percent of the federal poverty line and by prorating payment of benefits from the time of application.

Under current law, income limits vary according to the type of household, and a full month's benefits are paid an applicant, regardless of when the application is made.

Other provisions in the bill would permit states to set up voluntary workfare programs to require beneficiaries to pay back benefits, ban strikers from receiving stamps and prohibit federal spending on programs that encourage food stamp participation.

These were some of the key votes:

By voice vote, David L. Boren (D-Okla.) won an exemption from benefit cuts for households with persons 60 years of age or older or which receive Social Security disability or supplemental income payments.

By 69 to 30, Helms was defeated in a bid to ban indexing of stamp benefits -- periodic adjustments to compensate for inflation.

By 74 to 25, James A. McClure (R-Idaho) lost a proposal to count federal energy assistance, received mainly by the elderly, as income in calculating stamp eligibility.

By 56 to 36, Daniel Patrick Moynihan (D-N.Y.) lost in an effort to give Puerto Rico more time to set up the block grant system under which is now under must administer feeding programs, with reduced funding, as required by the bill.