Deputy Secretary of State-designate William P. Clark resigned from the California Supreme Court yesterday and could be sworn into the No. 2 State Department job as early as today, the State Department said last night.

Clark had held onto his $72,855-a-year judicial post even after being confirmed for his $50,112-a-year job by the Senate last month because he said he was involved in some cases that had yet to be completed. Clark, who was in San Francisco from Tuesday until Monday trying to wrap up business, said only one case is outstanding.

Clark had expected the case to be filed Monday, but it was held up, apparently by another justice, Mathew O. Tobriner. Tobriner, with Chief Justice Rose Elizabeth Bird, was on one side and Clark on the other in a personal conflict on the court that was widely publicized during a state investigation a couple of years ago.

Duties aside, one of Clark's last acts as a California justice was to attend a farewell dinner Sunday night. Tobriner and Bird didn't show up, but Clark refused to attach any significance to that.

And he was even able to kid himself during the dinner about his inability during his Senate confirmation hearings to answer some elementary questions about foreign affairs. In introducing his secretary, Bessie Wong, to the audience he said: "Bessie even knows the name of the foreign minister of Zimbabwe. The only problem was she forgot to tell me."