When Prince George's County Executive Lawrence J. Hogan sent his proposed fiscal 1981 budget to the County Council this week, he boasted about giving homeowners a 10 percent cut in their property taxes and holding government growth to 25 percent.

"I just want to remind everyone in here again: This is the largest tax cut in Prince George's County history," Republican Hogan said as he flashed a wide grin and stepped out from behind the prodium at a Monday morning press conference.

Meanwhile, Democrats on the County Council and in the legislature simmered over Hogan's boasts. They said that without the increase of $14.2 million in state aid the county received, Hogan, the only elected Republican in Prince George's, could not have cut property taxes by $12.6 million.

Obscured by the political posturing on both sides, Hogan's budget did include a set of cost-cutting measures that have begun to eat away at local government growth in Prince George's.

While it is uncertain what effect these changes will have on the delivery of services that grow costlier every day because of inflation, it is clear that Hogan's "waste-watcher" program is slowly but surely slimming, and trimming county government.

Under the administration of former County Executive Winfield Kelly, a Democrat, the county budget grew at a rate of 6.6 percent a year. Hogan allowed last year's budget to grow by 3.3 percent and this year's to grow only 2.5 percent.

The self-proclaimed tax-cutting budget-slashing county executive has instituted a series of measures that would make TRIM proponents smile and say: "There, I told you so."

First, he has centralized in his office all authority for filling vacancies in county government. By requiring county department heads to justify the hiring of new personnel and by putting pressure on the school board not to fill vacancies, Hogan has pared 932 jobs from next year's budget.

Many of the positions are open now. Those vacancies that must be filled are often given to part-time employes who are limited to working 700 hours or less in a year, and do not receive any of the fringe benefits that permanent employes get. About 335 positions were filled this year with 700-hour workers.

Hogan also has set up a desk in his office to take requests for volunteer work. Already during fiscal year 1980, Hogan's administratin has used 100 volunteers to temporarily fill vacant slots, including positions in the libraries, the fire department, and the office of emergency preparedness.

Other economy measures were noted in the budget. By using one carrier for employe life and health insurances programs instead of two, the county saved $400,000. The county saved $122,000 by cutting back on the amount of leased space for government offices.

Reorganization is another cornerstone of the Hogan budget-tightening program. For example, the Department of Public Works and Transportation saved nearly $300,000 after reorganizing and cutting 32 positions from its budget.

Hogan's budget also calls for a reorganization of the Department of Personnel and the Department of Program Planning and Economic Development later in the year.

Even overtime and sick leave use have not escaped Hogan's shears. Department heads have been told that they should be able to cut back on the use of both by monitoring employes more closely. The executive boasted in his budget message that the Department of Corrections had already reduced sick leave use 30 percent by requiring written excuses from doctors in some cases.

The school board, which has some degree of independence in setting its spending priorities, did not escape. Even though school authorities set their budget at $290.3 million, limiting its growth to 4 percent. Hogan cut another $4 million from the budget, called for the closing of 14 schools and elimination of 40 administrative positions.

The executive has also cut 20 positions from the 860-person Prince George's Police Department, and plans to request more help from the Park Police in protecting county citizens.

Hogan also estimates that his use of county operating funds to finance some of the capital improvement program will save Prince George's about $16 million annually because, unlike bonds, the money is interest-free

There are other plans on the drawing boards to further cut costs and improve efficiency in county government.

Department heads are asked to report to Hogan regularly on the progress they are making in improving efficiency and budget planners believe these reports will serve as a basis for future cost-cutting.

Talks are already going on between the executive's office and the school board on ways to save money by consolidating printing and vehicle maintenance services.