Sen. Edward M. Kennedy (D-Mass.) criticized President Carter's fiscal 1981 budget yesterday as "a harsh and insensitive document," and called for sharp cuts in proposed defense outlays and more spending for public service jobs.

In an eight-page critique, Kennedy said Carter's new budget "defies the great historic traditions of the Democratic Party" and "promises only more hardship for the poor, the sick, the cities, and above all, the unemployed."

Instead, he proposed his own spending plan calling for $3.4 billion more in antirecession job programs and $3.2 billion in added spending on a variety of social programs, from housing to child nutrition.

He also called for $1.4 billion in defense cuts, slashing money for the MX missile system and a nuclear aircraft carrier. And he proposed $5.9 billion in savings by repealing tax breaks for the oil and real estate industries.

Kennedy said that with all its additions and cuts, his proposal would result in a net saving of $500 million from Carter's plan, bringing the proposed deficit to $15.3 billion, from the $15.8 billion the president has proposed.

Like Carter, Kennedy omitted any proposal for a broad-scale income tax cut this year, preferring to allow taxes to rise to their highest level since World War II. Some of his proposals have been rejected by Congress before.