Mayor Marion Barry refused yesterday to identify the city programs and services that he is cutting back this year to try to avert a projected $110 million deficit because, he said, the public would be confused by all the budget numbers.

Barry told reporters he is reluctant to overwhelm citizens with data on the city's latest budget crisis at the same time the City Council is preparing a budget for the coming year and following closely the release of the city's financial audit for the 1982 fiscal year.

"I made the decision that really we ought to communicate better with people by not getting them confused with all these numbers," Barry said during a press conference at the District Building, his first in over two months.

Barry also said, during the wide-ranging session, that he opposes spending money to hold a special election to fill a Ward 1 vacancy on the Board of Education and that he would veto any attempt to scuttle the city's new mandatory no-fault car insurance law.

The school board could not agree Wednesday night on a replacement for former Ward 1 Board Member Frank Smith, who was elected to the City Council earlier this year. Several members have proposed that the City Council order a special election to fill the seat.

"The board rules require that they select someone, and it doesn't seem fair to now call for a special election and spend $40,000 to elect someone when the Board of Education itself ought to go and do what it ought to do," Barry said.

As for the controversial new car insurance law, Barry pledged to resist attempts to gut it before his administration has time to put it into effect.

The council approved a six-month delay this week in the effective date of the new law after the mayor said he needed more time to implement regulations governing rates. Some suporters of compulsory insurance said they were worried they might not be able to protect the measure against an anticipated attempt to repeal it.

But Barry said yesterday he would veto any bill that would either repeal or modify the existing language of the mandatory insurance bill, although it does not contain all the no-fault provisions he prefers.

"We intend to implement fully the bill passed by the council," Barry said. "You can rest assured we'll have compulsory insurance in the District of Columbia."

While he declined to say whether the general level of city services is being reduced to avoid a deficit this year -- promising to divulge the cuts after the City Council passes his proposed 1984 budget -- the mayor insisted that the city spared little expense in digging out of last weekend's major snowstorm.

More than $1 million of the city's $1.3-million snow removal budget was used up over the weekend to pay for plowing and spreading salt and sand.

"I think under very tough circumstances the [city] did a good job," Barry said. "There was no deliberate, as far as I know, cutting back of any snow plowers to save money. We're going to spend as much as is necessary."

For the coming year, Barry said he would hold fast to his budget proposal to spend $318.5 million on public schools, an increase over the current year's budget but less than the $336.4 million sought by the school board. He renewed his pledge to oppose a major tax increase in 1984, but said property tax rates might have to rise slightly.

On a separate matter, Barry said he was "genuinely concerned" that the new Washington Convention Center's food concessionaire was buying supplies from firms outside the District, a practice sharply criticized last week by council member Betty Ann Kane (D-At Large). However, Barry said he questioned possible political motives in raising the issue on the part of Kane, who challenged him for mayor last year.