Shortly after Teng Hsiao-ping's first press conference in China today, the three American network crews received an unusual request. Could they please cut the portion of the videotape showing the Chinese vice premier spitting loudly into his spittoon?

The networks complied. It was one more victory for China's most dynamic leader, preparing the way for his upcoming debut as a Washington media star.

An hour of give and take with 13 American reporters in the Big West Room of the Great Hall of the People strengthened a growing impression that Teng may already be a media freak.

He joked about photographers who always catch him smoking. He nodded knowingly as reporters were introduced, as if to indicate that he followed their dispatches religiously. He happily signed copies of the Time magazine cover showing him as "man of the year."

Like a press agent's dream, this veteran Communist answered the questions put to him with little more than a mixture of wild hopes and oft-repeated set pieces, yet the reporters lined up afterward to shake his hand.

The visiting American journalists, most of them hoping to live here some day, played their part by somehow fashioning news stores from his wisecracks and contradictions. Many also sidled up close during the handshaking to try to answer the burning question -- just how short is Teng? Answer: about 5 feet 2 inches.

The Chinese asked that the questions stick to the subject of Chinese-American relations, which Teng will be discussing with President Carter late this month at the White House. That meant questions about Taiwan, which Teng has been fielding lately with an unerring instinct for the soft answer that will make his Nationalist Chinese adversaries on the island absolutely livid.

Teng, 74, was asked if he expected to live to see the day when the mainland and Taiwan were reunited. He jumped at the chance to use the widespread interest in his health.

"My personal conviction is that the goal [of reunification] can be achieved this year," he said, hoping for what seems impossible. "As far as my health is concerned, I can at least live for 10 more years, but that's too long" to wait for reunification.

In what seemed to be a calculated attempt to raise media eyebrows, Teng referred to the Taiwanese president for the first time with an ordinary title of respect, instead of the usual reference to the "Chiang bandits" on the island.

"We will be taking a variety of measures in different forms to discuss with the Taiwan authorities, particularly Mr. Chiang Ching-kuo, the question of the reunification of the motherland," Teng said.

Like most Chinese realists, however, he probably realizes that such talks are years away.

When asked if China planned to send more arms and advisers to its beleaguered ally, Cambodia, Teng said, with a straight face. "They don't need any advisers from us, because they have their own rich experience."

His answers to questions about Chinese intentions to take Taiwan by force were carefully phrased and much qualified, suggesting that he had read press accounts of his Tuesday meeting with U.S. congressmen during which he came close to promising there would be no invasion.

"We wish to solve this question by peaceful means, but whether or not this can be done is a very complex problem, We cannot assume any undertaking that no other means other than peaceful means will be used to achieve reunification of the motherland. We cannot tie our hands on this matter," he said.

The Chinese got a taste of the occasional failings of the U.S. media, which will soon have permanent bureaus here. One news agency account, dispatched minutes after the press conference ended, said Teng had threatened to use force on Taiwan if reunification did not come in 10 years.

American diplomats were upset by the distorted account, which they feared would be widely circulated in the United States and disturb the Chinese. One Chinese Foreign Ministry official just laughed when told of it, however, as if he expected no better from the bourgeois journalistic front.

About 27 American reporters and television technicians are here on special two-week visas. All are scheduled to leave China Jan. 12, but John Roderick of the Associated Press and Robert Crabbe of United Press International have been told they may stay an extra two weeks.

An official of the Foreign Ministry's information department told representatives of the two news agencies that they will be the first U.S. news organizations to be allowed to open permanent offices in Peking. In exchange, the United States will allow reporters of the official New China News Agency to live in Washington.

The Chinese correspondents may get there in time to watch Teng confront American journalists on their home ground, where they are more numerous and unintimidated by the proletarian grandeur of an audience in the Great Hall of the People. Teng said today he was looking forward to the trip and he tried out a few answers to questions that he will probably be asked when he faces cameras in the United States.

Since Sen. Barry Goldwater (R- Ariz.), a leading opponent of the U.S. switch in relations from Taiwan to the mainland China, does not seem to have accepted Teng's recent invitation to visit Peking, will the vice premier talk with the senator in Washington?

"No.I will not talk with him in Washington," Teng said. "If the opportunity arises of meeting him there, I will extend a personal invitation to him to come to Peking and discuss this question. Our major hope is for Mr. Goldwater to get to know about China."

What about human rights in China?

"It is my hope that we will not discuss this question [in Washington] for each has their own explanation or interpretation of human rights," Teng said. "We are trying to give full play to democracy. We are making great efforts in this regard."

Teng then coughed up a contribution for his spitoon with such a loud noise that his interpreter's English translation had to be repeated.