Secretary of Health, Education and Welfare Joseph A. Califano Jr. was attacked yesterday by former HEW secretary Wilbur J. Cohen for engineering the "tragic, unsound, immoral, unjustified" cuts in Social Security benefits which President Carter is expected to propose in his budget next week.

"Califano is making Social Security a political football," Cohen charged, speaking at a meeting of 20 organizations of the elderly gathered to protest the cuts. Cohen said Califano "wants Congress to renege on the social compact [and] break faith with the American people."

William Hutton of the National Counsel of Senior Citizens said, "The administration budget proposals" amount to "a rape of the Social Security system."

Critics of the cuts fear they are only the first in series of slashes designed to save money.

Cohen said that Califano, in his zeal to show that he can reduce his department's outlays, is ignoring "the fundamental principles under which Congress established this system.... The whole idea of this system is that it should be outside" the ordinary budget and secure from temporary political decisions to cut federal spending. "That's why it's financed by [an earmarked] payroll tax."

"Cap Weinberger looks like a raving liberal [compared] to Joe Califano," said Cohen, referring to an HEW secretary noted for his budget cutting in the last Republican administration.

Califano had no personal response but an aide said: "It hardly seems reasonable that anyone who understands our proposals could accuse the administration of attacking the fundamental principles of Social Security.Our proposals deal with a few outmoded benefits, most of which will be converted to a sounder form and all of which put together amount to less than 1 percent of the [$100 billion in annual] Social Security benefits."

Hutton and spokesmen for the American Association of Retired Persons, the American Association of Homes for the Aging, the National Caucus on the Black Aged and other groups representing the elderly met with Califano and aides Thursday night to protest the $600 million in fiscal 1980 benefits cut (which will gradually rise to $6.5 billion a year by 1985) expected to be in Carter's budget proposals.

They said Califano refused to budge on the various cuts which they said include elimination of the $122 minimum benefit, elimination of the $255 lump-sum death-burial benefit, eliminating benefits for a surviving child of a deceased worker at age 18 and cutting disability benefits levels.

Dr. Dolores Davis, director of the National Center on Black Aged, said the cutoff of survivor benefits at 18 for students "will have a devastating effect" on black youth and other minorities. She quoted Califano as saying such youth should seek student loans or grants from HEW. At present children of deceased workers may receive benefits until age 21 as long as they remain in school.

Cohen called repeal of the $255 death benefit "one of the cruelest and most misinformed proposals I have ever seen," since many minority families simply haven't the money to pay for burial, which can run $500 or more.

Cohen and others were particularly critical of Califano for recommending changes to Carter without first consulting various existing study commissions on Social Security -- a move which Cohen said is unprecedented.