The House Appropriations Committee began systematically slicing into Gov. Harry Hughes' $6.4 billion budget today as part of a strategy to avoid the politically painful step of increasing taxes on property, cigarettes and alcoholic beverages, as the governor had proposed.

Speaker Benjamin L. Cardin said the cuts--about $24 million expected in voting sessions today and Thursday--are legitimate reductions that will not harm services, and will doom the need for Hughes' tax initiatives.

"Our objective in cuts is to do what's right from the standpoint of legislative review and we have no objective in terms of dollars," Cardin said, adding, "I'm pretty optimistic that we can avoid the taxes ."

While Cardin maintained that the budget-cutting fervor is not solely to avoid tax increases, Appropriations Committee members were less insistent on that interpretation, with some singing, "tax avoidance, we got a little tax avoidance," as they convened for the budget cutting meeting.

Cut today were requests for travel allowances, secondary positions, operating funds for Washington Metro, funds for higher education, including $1.3 million in merit increases for University of Maryland faculty members, and veterans programs. The more controversial cuts are expected Thursday, when the committee considers funding for health and environmental programs, nuclear-power-plant siting, open-space preservation, Medicaid reimbursement and state employe health benefits.

Hughes' fiscal 1984 budget was submitted to the legislature last month with $22 million in proposed "sin tax" increases on cigarettes, beer, wine and liquor and $16 million increase in the state property tax to offset a projected $133 million deficit.

Since then, legislators in the House and the Senate, heavily lobbyied by the taxed industries and others, have said they would like to balance the budget--as required by the state constitution--without the new taxes.

The Senate Budget and Tax Committee took the lead last week when it voted to cut $22 million instead of raising the "sin taxes." The House, apparently not to be outdone, responded this week with a decision by the leadership and the Appropriations Committee to search for $38 million--the amount of the sin tax and property tax increases together--in cuts or alternative revenue raisers, such as new fees.

Hughes, meanwhile, has insisted the cuts in his "stand pat" budget can only hurt services and citizens.

Both the legislature and the governor are also hoping the the revenue estimates to be released next week will show that the state's economy--and tax collections--have picked up, bringing unexpected money into state coffers.

But such optimism was not the keynote of the House committee meeting today, where delegates reviewed subcommittee reports for several hours to decide what should be retained in the budget that goes to the House floor Monday.

Del. R. Clayton Mitchell (D-Kent), the committee chairman, said the expected cuts are double what the committee made last year.

The committee cut travel allowances for dozens of boards and commissions, from the Maryland Racing Commission to the state athletic examiner, and eliminated at least 80 positions from law clerks for judges to secretaries. It struck $48,000 in proposed merit increases for Baltimore court workers.

The committee also agreed to eliminate the Nuclear Civil Protection Planning program.

"For these people to do the monumental tasks we've given them with three staff positions and $77,000 is ridiculous," Del. Paul Muldowney (D-Washington) said after reading a passage from the budget book that described the program's task of moving, feeding and protecting 3 million Marylanders. "Since we can't raise the amount the legislature can only retain or cut the governor's budget proposal , let's just cut it."

The committee also cut nearly $444,000 allotted to pay bounties to those hauling abandoned cars off state roads, a program that the House had tried to kill for several years and lobbyists have managed to work back into the budget through the Senate or conference committees.

The committee also agreed to end funding for the Occupational Disease Control Board of the Workman's Compensation Commission, which is scheduled to be phased out this year despite vigorous lobbying efforts by business lobbyists.