President Reagan's controversial nominee for deputy secretary of state, William P. Clark Jr., got a rough going over yesterday from Senate Democrats who seized on his admission that he knows very little about foreign policy to hit him with a barrage of questions he was unable to answer.

Although the Republican majority in the Senate is expected to ensure Clark's confirmation, his hearing yesterday before the Senate Foreign Relations Committee saw the California Supreme Court justice forced to respond repeatedly with "I don't know" or "I'm not in a position to say" to questions covering a broad range of foreign policy issues.

Focusing on the argument that Clark is supposed to be the "alter ego" of Secretary of State Alexander M. Haig Jr., the Democrats drew from him the admission that he cannot identify the prime ministers of South Africa or Zimbabwe, is unaware of the issues involved in U.S.-Brazilian relations, knows nothing about the internal affairs of the British Labor Party and is unaware of attitudes in Western Europe about deployment of new U.S. missiles there.

When his questioners turned away from the factual matters to ask Clark's opinion on various issues, he balked at responding, in almost every instance, on the grounds that he didn't know enough about the subject or was not aware of the positions held by Haig or the State Department.

Among other things, he was asked how he regards the status of Jerusalem and Israeli settlements in Arab-occupied territory, whether he thinks the United States should recognize the government of Taiwan and whether he favors cuts in U.S. foreign aid. Each time, he replied by saying "I do not have a person view" or "I do not have a position on that at this point."

It was a performance that finally provoked an expression of exasperation from Chairman Charles H. Percy (R-Ill.) who, with other Republicans, had tried hard to steer Clark's testimony into channels where he could demonstrate his qualifications.

Percy noted with asperity that Clark had failed to heed his admonition not to appear before the committee without first boning up on Reagan's foreign policy positions as enuciated in the presidential campaign, on Haig's testimony in his confirmaiton hearings and on the Cater administration's agreements with Iran governing the release of the American hostages.

In his opening statement and subsequent testimony, Clark freely conceded that his experience in public life -- first as chief of staff to Reagan when he was governor of California and then as a jurist -- had given him no grounding on foreign policies.

But, Clark added, he believes he can learn what is required; and, in a point he stressed repeatedly, he said Reagan had chosen him for the State Department's second-ranking job on the basis of his abilities as an administrator. It was his understanding, Clark said, that his main function would be to apply these administrative talents to seeing that the department functions efficiently.

Clark, regarded as one of the people personally closest to Reagan, told the committee he had been sounded out by the president's aides about his willingness to be considered for three major posts -- attorney general, secretary of agriculture and director of the Central Intelligence agency -- and had said he preferred to remain on the California Supreme Court.

He added that it was only when presidential counselor Edwin Meese III visted him and said Reagan wanted him to accept the deputy secretary's post that he agreed to come to Washington.

But as Sen. John Glenn (D-Ohio) said on behalf of committee democrats, "We look at you as a pseudo secretary of state. We don't look at you as just an administrator making sure the trains run on time around the State Department."

Sen. Claiborne Pell (D-R.I.), who described Clark as "one of the most forthright and engaging witnesses ever to apear before this committee," said he appeared "perfectly suited" to the job of undersecretary for administration but added that the deputy secretary had to be equipped to step in as a policy maker when needed. Sen. Joseph Biden Jr. (D-Del.), who was the most persistent in asking Clark factual questions he was unable to answer, kept referring to him as a "very nice guy," and adding: "I really wish I didn't have to do this to you."

Republican committee members stressed Clark's administrative abilities and influence with Reagan, and argued that past deputy secretaries of state had come into office with little foreign policy experience. That led to several exchanges between Democrats and Republicans about the respective experience of various past occupants of the job.

The committee is scheduled to vote on the nomination this morning; most congressional sources predicted that, despite the mauling Clark was given, he will pass muster with the committee and the full Senate, with only a handful of Democrrats voting against him.