The Alexandria School Board endorsed last night the establishment of a proposed public "teen clinic" that would distribute free contraceptives to students at the city's only high school.

By a vote of 6 to 2 with one abstention, board members passed a resolution in favor of opening a clinic in or near T.C. Williams High School that would "meet the needs of all Alexandria adolescents." Though the resolution did not specifically mention birth control devices, the board members who voted for it said they favored the proposal.

The City Council will have the final say on whether the clinic is built, and plans to take up the issue early next month. But the facility has become the city's dominant political issue already, prompting a strong outpouring of sentiment on both sides.

Those emotions boiled over again last night when Board Chairman Timothy Elliott announced early in the meeting that the public would not be allowed to speak on the subject. The School Board and City Council held a joint six-hour public hearing on the clinic Tuesday.

Most of the 75 people attending the meeting had turned out to address the clinic issue, and there was a brief but angry outburst that forced Elliott to gavel the meeting to order.

"I didn't want to speak about the clinic itself, because we had done that at the hearing; I wanted to speak about the vague wording of their resolution," said Marjorie Mulloy, president of the anticlinic group, Concerned Alexandrians for Responsible Education.

"The wording of the resolution is so nebulous that it doesn't address the primary issue: whether to provide birth control devices. I don't think the board has ever limited debate like this before. It seems to me that voicing an opinion is the right of the public."

But School Board member Judy Seltz, who introduced the motion supporting the clinic, said that those who voted for the motion understood what they were voting for. "Nothing else was at issue," Seltz said.

"Our kids need the clinic," she said. "The emotional, social and fiscal costs of teen-age pregnancy are overwhelming."

Elliott, who abstained on the issue, said he agrees with City Council member Carlyle C. (Connie) Ring Jr., who opposes the clinic. "We need to reinstill moral values in the country so teens don't have sex and get pregnant," Elliott said. "That is only part of what the clinic would be about, but it is all of what this debate is about."

Board members Seltz, Gia Adams, Leslie Hagan, Sandy Lindsay, A. Melvin Miller and Lynnwood G. Campbell Jr. voted for the clinic. Members Nelson E. Greene Jr. and Gene Lange opposed it, and Elliott abstained.

The controversy over the clinic began with a city study 18 months ago, but picked up steam this fall when state statistics showed that Alexandria's 1986 teen-age pregnancy rate was the highest in the state.

In the last two weeks, clinic opponents have spent more than $7,500 on radio and newspaper ads, while supporters mounted a smaller newspaper campaign. Opponents also have inaugurated a political action committee that they say will "screen" candidates for mayor and the City Council next May.

The Catholic Church has been heavily involved in the debate. The Diocese of Arlington, which includes most of Northern Virginia, issued a statement opposing the facility, and all of Alexandria's Catholic churches asked for prayer on the issue in masses Sunday, Monday and Tuesday.

In many ways the clinic is an outgrowth of city policies already in place. The school system has an extensive sex education curriculum. The city Health Department provides birth control devices and information at a clinic across town from T.C. Williams, and a half-mile from the school, a nonprofit clinic in a Methodist Church offers the same services.

But the explosive nature of the issue rubbed nerves raw. "Some of you have said that . . . we're being mealy-mouthed," said board member Miller, who supported the clinic.

"Well, I'm not being mealy-mouthed. I have no problem whatsoever with the clinic dispensing contraceptives."