In light of the D.C. government's severe financial crisis, the mayor has trimmed the planned budget for the D.C. Commission on the Arts for fiscal year 1981 -- which begins October 1 of this year -- by $24,200.

The commission, a D.C. government agency which award grants to local arts groups and individual artists, originally had been granted $617,000 when the budget was acted on by the City Council. That was before the District government asked all of its agencies to take cuts.

"Our amended request is $592,900," Mildred Bautista, executive director of the commission, told the arts commissionrs at a meeting last night. "I think we can live with that," she told them. "We're one of the agencies minimally touched. We'll cross our fingers and hope we won't be touched again."

Peggy Cooper, chair of the D.C. Commission, was less resigned to the cuts. "The fact of the matter is we're inadequately staffed," Copper said at the meeting.

The D.C. City Council will hold budget hearings in the next week and later act on the budget. The commission is not scheduled for a hearing, but, Bautista said, the council "could cut more or less" from the commission's budget.

The District budget office is taking most of the $24,200 cut from a category called "services and charges" which includes postage, printing and duplication, and local and out-of-city travel. It is also cutting funds allotted for office equipment.

Another $1,200 will be cut from "grants and subsides." No money at all will be cut from pay increases.

All of these funds are separate from the basic state operating grant which the commission will receive from the National Endowment for the Arts, which will probably be in the same amount that it received for the current fiscal year -- $295,000.

At least night's meeting the commission also approved settling up with the National Symphony Orchestra an unusual apprenticeship program.

Under the program, up to five District students will be selected through auditions this summer to receive intensive tutoring by the orchestra musicians over a period of years. The students would be encouraged to attend concerts and rehearsals.

After the student went off to college or a conservatory, he or she would return in the summer months for continued training and eventually would have an opportunity to serve as an apprentice in the National Symphony Orchestra.

The commission plans to commit $20,000 to the program this fiscal year and continue to fund it each year.

"This is a first in the country," said Cooper last night to the commissioners. "Every symphony has been criticized for lack of minority participation . . . This is definitely something I think is right."