President Reagan denounced as "a cruel hoax" yesterday the so-called domestic-content legislation pending on Capitol Hill that would require most automobiles sold in the United States to be manufactured with a certain percentage of U.S. parts and labor.

In his regular Saturday radio broadcast from Camp David, the president vowed to "continue to oppose quick-fixes of protectionism" in world trade and singled out for criticism the domestic-content bill, which is expected to come up for a vote soon in the House Energy and Commerce Committee.

The domestic-content legislation would require any auto maker selling more than 100,000 cars and light trucks in this country to produce an increasing percentage of each vehicle in U.S. plants. Cars with the largest total sales would be required to contain at least 90 percent American-made parts.

The legislation, which passed the House last year over Reagan's objections but died in the Senate, is backed by the United Auto Workers union as a way to protect American jobs against foreign competition. Owen Bieber, president of the 1.1-million-member union, said yesterday that domestic-content legislation should be one part of a "sensible, realistic industrial policy" for the United States.

"Without such a policy--involving government, business, labor and the public--I believe we will see continued economic stagnation and drift which our nation and its people simply cannot afford," Bieber said in remarks prepared for the Americans for Democratic Action convention here.

Reagan insisted that the domestic-content bill would not produce the intended result.

"New cars would be more expensive and more jobs would be destroyed than protected," he said. "We would buy less from our trading partners, they would buy less from us, and the world economic pie would shrink. Recrimination and retaliation would increase."

The president also reaffirmed his promise to veto tax increases while the economy is recovering. " . . . Let there be no misunderstanding my position," he said. "Hard-working families are already overtaxed. And you know I'm not just whistling in the dark . . . . We don't need tax increases. We need spending restraint."

Rep. George Miller (D-Calif.), delivering the Democratic response to Reagan's speech, said improved education is one of the most important factors in achieving economic recovery and improving the U.S. position in international markets. He assailed the president's record on education issues.

Reagan opened his radio speech yesterday with an appeal for contributions to the American Red Cross, saying efforts to cope with bad weather have "exhausted" its budget.