The Reagan administration came to town with the well-publicized goal of abolishing the Education and Energy departments that former president Carter created.

And while it has no plans to abolish the Labor Department, it is managing to hollow out that agency by cutting its budget, its staff and its regulatory and enforcement efforts.

None of the department's three basic components--unemployment compensation, manpower programs and workplace regulation--has escaped unscathed.

Unemployment compensation, including the trade adjustment assistance program that pays U.S. workers who lose their jobs because of foreign competition, consumes most of the department's funds. Under Carter, unemployment insurance would have cost the government $23.5 billion in fiscal 1981, with trade adjustment assistance taking nearly $2.9 billion more.

But at President Reagan's request, Congress cut the first, mainly by limiting conditions under which benefits can be paid beyond 26 weeks, and has nearly abolished the second.

Manpower programs, in the department's Employment and Training Administration, usually took most of what was left of the department's budget after unemployment benefits. Under the 1973 Comprehensive Employment and Training Act (CETA), the department funneled money to state and municipal governments for public service work.

But the public service employment program, 340,000 jobs valued at $3.1 billion, has vanished along with nearly $600 million in related training and support projects.

In all, a Labor Department that would have spent $37.6 billion in fiscal 1981 under Carter will spend $26.5 billion under Reagan--or 29 percent less--if the president gets all of the budget cuts, including the additional 12 percent reduction, he wants for 1982.

The demolition also has affected the regulatory side of the department, which oversees some 134 federal laws--"one of the most extensive set of regulatory programs in the federal government," according to former Labor secretary John T. Dunlop.

While the regulatory programs take less than 2 percent of Labor's budget, they are staffed by 85 percent of the department's workers.

Regulators work in Labor's Employment Standards Administration, which administers federal wage and hour laws, equal opportunity hiring rules, and workers' compensation programs. Others work in the Occupational Safety and Health Administration, the Mine Safety and Health Administration, and the Labor-Management Services Administration, which, among its other duties, regulates private pension and welfare plans under the 1974 Employe Retirement Income Security Act.

Carter had planned $807 million in regulatory spending for fiscal 1981. Reagan cut that to $786 million and is now proposing $742 million for fiscal 1982.

Cutting the regulatory budget means cutting jobs--about 2,000 jobs for every $100 million budget cut, according to department estimates--because most of the money there goes for salaries.

In December, 1980, 22,054 people were full-time Labor employes, about 18,000 of whom--clerical workers, researchers, enforcers and policy makers--were involved in regulation. The department lost 900 full-time workers last fiscal year and, before Reagan's request for 12 percent more in budget cuts, was planning to lose 308 more full-time workers in 1982. That means overall full-time employment at Labor could, at the least, fall to 20,846 people, a 5.5 percent drop since 1980.

Department records show that most full-time employes leaving the department--through retirement, resignation or "reductions in force"--are from regulatory agencies. Examples: OSHA lost 160 of its 2,786 workers last fiscal year and was scheduled to drop 90 more in fiscal 1982; the Employment Standards Administration lost 225 of its 4,942 jobs last fiscal year, and was slated to lose 75 more in fiscal 1982, and the mine safety division was scheduled to lose 235 of the 3,562 workers in its division in 1980.

Among Labor's nonregulatory agencies, the Employment and Training Administration, which had 3,290 workers in 1980, will suffer the most job cuts. The division dropped 160 jobs last year, and was scheduled to lose 46 more in fiscal 1982. Much larger staff cuts throughout the department are anticipated if the 1982 budget is reduced further.

The figures mark an unmistakable shift to the philosophy that government hould be doing less. OSHA is a dramatic example of the philosophy in action:

OSHA work place inspections declined 17 percent--from a monthly average of 5,680 between January and October, 1980, to 4,703 between February and August, 1981.

Average monthly follow-up inspections dropped 68 percent, from 1,012 a month to 326 during the same period.

Citations for violations have also dropped as inspections declined, down an average 27 percent per month for "serious" health and safety violations.

Last May, the department disallowed "walkaround pay" for workers participating in plant inspection tours with OSHA officials.

The department has sought to stay, rescind or modify proposed and existing regulations setting standards for employe exposure to chemical and other work place hazards, such as noise, lead and cotton dust.

In his first news conference on March 10, Donovan said the president's economic program "is one of hope, not despair" and that the department's contribution towards its success would be "a major one, not merely in dollars cut from programs and projects, but . . . in terms of a growing economy that will leave no American working man or woman behind."