Robert A. Derzon, Health, Education and Welfare Secretary Joseph A. Califano's choice to reorganize and reform Medicare and Medicaid, was fired this week for not doing the job fast enough.

He accepted Derzon's resignation yesterday as head of HEW's 18-month-old Health Care Financing Administration (HCFA), the Califano vechicle to try to make the $36 billion Medicare and Medicaid programs more "cost-effective."

Derzon aides said Califano asked for the resignation Monday night, following a series of sometimes fiery-clashes in recent months.

Yesterday Califano said he is replacing Derzon, 47, formerly one of the nation's leading hospital administrators, with his assistant secretary for management and budget, 33-year-old Leonard D. Schaeffer.

It was Califano's first top-level replacement of one of his own people, the people he called "new blood." After taking office last year he rapidly fired a series of officials whom he called "old blood" that needed replacing.

Califano aides agreed yesterday that he felt Derzon was "not moving fast enough" to unify the mammoth Medicare and Medicaid programs, and "the secretary is a man who likes to move."

Derzon aides agreed that this had been an issue. But they also said Derzon - administrator until 15 months ago of the University of California-San Francisco hospitals and clinics - "was a man willing to tell Califano "That's not right" or "That won't work."

"Califano doesn't like that," they said.

"Derzon is a strong man and Califano doesn't like other strong people around," said one HCFA official. "And Derzon wasn't willing to go out and say the health industry was bloated and hospitals were ruthless and stealing the public blind, which Califano was saying."

When the administration failed to have Congress put a tight lid on hospital cost increases, said other officials. Califano tried to get Derzon to tighten payments to hospitals by new ways of regulation. But again, said the officials, Derzon refused to move quickly enough to satisfy his boss, often claiming that hasty actions might be unwise.

"I think it was a difference in personality," said a Derzon aide.

But a Califano aide said, "I don't think personality was involved. There were no real policy disputes. But Califano wanted someone with experience in large scale financial management to complete the job of putting Medicare and Medicaid together."

In any case, said another officials, "I wasn't surprised. At some meetings Califano was really yelling at Derzon." Six months ago the National Journal quoted an HEW official as saying Califano "beats on Derzon's head at every turn, demanding to know why HCFA cannot move faster."

Medicare pays hospital and medical bills for Americans 65 and over and some Medicaid helps states pay such bills for the poor.

Until March 1977 they were run separately, with often conflicting policies, within huge HEW. When Califano combined them in HCFA, he said he hoped for significant savings.

Whether that will happens is still unclear. The programs cost the federal government $31.3 billion in fiscal 1977, and are estimated to cost between $35.6 and $36.4 billion in fiscal 1978, meaning a $13.7 to 16 percent increase.

Derzon's deputy administrator, William Fullerton, resigned this month. But associates said his main reason was financial and he will remain an active HEW consultant. "Still," said another Derzon aide, "I don't think he would have quit if things had been going well."

Califano said his executive secretary, Frederick M. Bohen, will replace Schaeffer as management and budget chief, and Bohen will be succeeded by his deputy, Richard Cotton.

Until joining HEW, Schaeffer was a Citibank of New York financial vice president. He became vice president of an investment firm in 1971, just two years after graduating from Princeto, then in quick succession a management consultant for Arthur Anderson & Co., deputy director of the Illinois state department of mental health, Illinois' budget director, a Citibank officer and an HEW star.