President Carter began the promised reconstruction of his administration yesterday by firing Treasury Secretary W. Michale Blumenthal and Health, Education, and Welfare Secretary Joseph A. Califano Jr.

More Cabinet changes, including the resignation of Energy Secretary James R. Schlesinger Jr. and the dismissal of Transportation Secretary Brock Adams, are expected to be announced today.

In a series of terse statements market the breakup of the original Carter Cabinet, White House press secretary Jody Powell said the president will nominate Federal Reserve Board Chairman G. William Miller to replace Blumenthal and Housing and Urban Development Secretary Patricia Roberts Harris to replace Califano.

Powell also announced that Carter will nominate Deputy Attorney General Benjamin R. Civiletti to replace Attorney General Griffin B. Bell. Bell long has said he intended to leave the Justice Department before the 1980 presidention campaign and, according to Powell, will remain at his post until Civiletti is confirmed by the Senate.

No successor to Harris at HUD was announced immediately.

The upheaval in the Cabinet is expected to be completed by the time Carter leaves for the presidential retreat at Camp David, Md., today at mid-afternoon. Changes in the White House staff, also vowed by the president, are not expected to be announced until next week.

Reaction on Capitol Hill to the day's events was almost universally negative as Democrats and Republicans complained that Carter was undoing the good he had done himself in his speech to the nation Sunday night. Members said that, while in his speech the president had given the impression he could manage a crisis his actions yesterday created a new crisis for the administration.

But at the White House, the most extraordinary day of the Carter presidency appeared to unfold according to plan as every two hours or so Powell dressed in a dark blue, three-piece suit, emerged from his office to annouce the departuer of another Cabinet secretary.

Califano and Blumenthal, both outspoken and independent with powerful enemies on the White House staff, clearly had been targeted for dismissal.

Adams, however, was to have survived the purge until he issued a statement yesterday virtually asking to be fired. He apparently will get his wish today.

Sources said that yesterday morning Hamilton Jordan, the newly designated White House chief of staff, told Adams the president wanted him to remain in the cabinet but that he would have to get rid of at least two of his top assistants. Admas replied that he would have to think about that, the sources said.

Later yesterday in Cambridge, Mass., Adams issued a statement saying he had been asked to remain and was "considering whether or not I should." He said his decision depended on a number of factors, including the administration's commitment to mass transit, his continued access to Carter and "the responsiveness of those with enhanced authority in the White House staff to the Congress and the American people" - an obvious jab at Jordan's new role as chief of staff.

Adams is believed to be considering a Senate race in his home state of Washington, possibly accounting for his decision to break ranks with the administration.

Schlesinger, like Bell, it not to be fired but is to have his plans to leave the government offically announced today. All but conferring this, Powell said last night:

"Secretary Schlesinger has asked to resign or leave twice. As Secretary Schlesinger indicated earlier this week, he does plan to leave by sometime this fall. The date will be determined by the president and the secretary, but until that date he has the president's full confidence and support."

The White House also is expected to announce a successor to Schlesinger today.

Announcements that Bell and Schlesinger are leaving the government - while clearly different from the firings of Blumenthal and Califano - apparently are being made at the same time to give Carter a clean break in the makeup of his administration, accomplished over a stunning 48-hour period.

Speculation on new appointments to vacant posts began immediately. Mentioned as possible successors to Harris at HUD were Mayor Richard Hatcher of Gary, Ind., and Mayor Tom Bradley of Los Angeles, both of whom are black as is Harris and former mayor Moon Landrieu of New Orleans.

Deputy Defense Secretary Charles Duncan Jr., a former head of Coca-Cola, has been chosen to replace Schlesinger at the Energy Department, the Assocciated Press said last night.

"It's cut and dried," said one source, indicating that the announcement may occur today. Duncan, reached at his Washington home, declined to confirm or deny the report.

Meanwhile, there were reports of the Carter-ordered shakeup spreading through the subcabinet level of the government. Today is the deadline that Jordan set for return to the White House of "evaluation forms" on White House staff aides and subcabinet officials. If Jordan's demand to Adams that he fire at least two of his top Transportation Department assistants is indicative of White House intentions, the shakeup could be extensive.

The president set the stage for yesterday's developments on Tuesday when we extracted resignation offers from the Cabinet and White House senior staff, a total of 34 persons. He promised then to act on the offers "expeditiously."

More than anything, yesterday's firings and those expected today appeared to be a move by the Carter White House to assume complete political control over the administration under the direction of new chief of staff Jordan and other senior presidential aides from Georgia. For more than a year, senior White House aides have been complaining that Carter's original approach to government - stressing the independence of Cabinet secretaries, many of whom had almost total freedom in choosing their top assistants - was a costly mistake that left the White House impotent to implement presidential decisions.

That approach, which was tinkered with in Carter's second year as president, was brought to a complete halt yesterday.

White House officials did not attempt to explain the firings of Blumenthal and Califano. In both cases, Powell said only that Carter is "engaged in a process of review and evaluation, that the purpose of that process is to make decisions that will best equip the administration and prepare the administration to deal with the problems which face the country...."

Califano's dismissal, rumored for days, came as no surprise. Blumenthal had also figured in such speculation, but was thought to stand a better chance of surviving becauce of his standing in the business community and the impact his firing would likely have on the already shaky status of the dollar.

In his speech Sunday night, the president set the criterion for yesterday's action. Recalling the advice and criticism he received at the Camp David "domestic summit conference," he quoted one visitor to the presedential retreat as telling him, "Some of your Cabinet members don't seem loyal."

That was the charge most often leveled by senior White House aides against Blumenthal and, especially, Califano, whom some Carter aides considered too close to Sen. Edward M. Kennedy (D-Mass.), a potential reval next year for the Democratic presidential nomination.

The president appeared in public only once yesterday and that was before any firings were announced. Speaking to a group of young people from the Future Farmers of America in the White House Rose Garden, Carter said he was undertaking "an intense effort to review my own rule as president and the makeup, the constitution of my government..."

"I will make the tough decisions that are necessary for improvements, and I know that you as leaders understand that quite often decisions of a leader are not easy."

Shortly after noon, just 25 minutes before Califano was to begin his news conference, Powell appeared in the White House press briefing room with the first of the day's announcements: the firing of Califano and his replacement by Harris.

Powell quoted Carter as saying that Harris "has established an admirable record of efficient and compassionate leadership at the Department of Housing and Urban Development. She has my full confidence and support as she begins to assume the responsibility for leading the department which more than any other directly touches the lives of those who must depend upon government."

Powell also released copies of letters between the Carter and Califano, who had met together at the White House Wednesday and again yesterday.

In his letter, Califano said it had been "a deeply and satisfying experience" to administer many of the "Great Society" programs enacted under President Johnson, whom Califano served as a White House aide. He concluded by wishing Carter well "as you continue striving to fulfill the enormous responsibilities of your office, to build upon your achievements, of which you can be justly proud."

In his handwritten letter, addressed "To Secretary Joe Califano," the president said he accepted the HEW secretary's resignation "with a genuine feeling of appreciation and of recognition for your notable accomplishments."

News of the sacking set off a series of tributes to Califano no Capitol Hill. In a statement indicative of the general congressional reaction, Rep. David Obey (D-Wis.) said Califano's dismissal "is a victory for mediocrity."

At least one politician had a favorable reaction yesterday to Califano's ouster. "You don't see me crying," said North Caolina Gov. James B. Hungt. "I hope Mrs. Harris will be more fair...."

Califano has angered many North Carolinians with this stands on school desegregation and tobacco.

There was a certain irony in Carter's choice of Harris to succeed Califano, who has much in common with her. Like Califano, Harris is a lawyer, is a longtime Washington figure, is far from being a government "outsider," and has deep roots in the liberal wing of the Democratic Party.

Even in the White House there was general recognition of Califano's skills in administering the sprawling bureaucracy of HEW. Harris, like Califano, has annoyed some White House aides with acts of outspoken independence, and has not been praised for her administrative ability.

As the day progressed, Blumenthal slipped into a side entrance of the White House in early afternoon for a meeting with the president. He left at about 2:15 p.m. and was described by one observer as "white as a sheet," and by another as "looking glum, chomping on his cigar."

At 3:30 p.m., Powell made the announcement about Civiletti succeeding Bell. There was no exchange of letters as Powell portrayed the attorney general's resignation as the fulfillment of a longstanding understanding between him and Carter. Schlesinger's resignation is expected to be handled in a similar manner today.

An hour later, Powell announced the firing of Blumenthal and his replacement by Miller.

Powell quoted the president as saying that as chairman of the Fed, Miller had "established a reputation at home and abroad that will enable him to provide strong, effective leadership for our economic policy. He has demonstrated a firm commitment to the defense of the dollar, sound economic policy, the fight against inflation and strong measures to deal with our energy problem. He has may confidence and support."

The White House also released an exchange of letters between Carter and Blumenthal.

In his letter, Blumenthal called the choice of Miller to succeed him "excellent," and urged Carter "first and foremost" to continue to fight inflation through "tight fiscal policy, strict controls on government spending" and other measures. He pleged "wholehearted support" for such policies.

The president's handwritten reply was longer and considerably warmer than his letter to Califano. He cited the treasury secretary for "excellent service" and said the policies he pursued "have been right and necessary."

"You have served the nation well during a difficult period," Carter wrote, adding: "Mike, you have been a leading example of the readiness of prominent Americans from the private sector to render services in the public interest. As you reutrn to private life, you have my personal best wishes for the future and my thanks for your distinguished service."

The nominations of Harris, Miller and Civiletti are subject to Senate confirmation. CAPTION: Picture 1, In, WILLIAM MILLER, Treasury; Picture 2, Out, MICHAEL BLUMENTHAL, Treasury; Picture 3, In, BENJAMIN CIVILETTI, Justice; Picture 4, Out, GRIFFIN BELL, Justice; Picture 5, In, PATRICIA HARRIS, HEW; Picture 6, Out, JOSEPH CALIFANO, HEW; Picture 7, ?, JAMES SCHLESINGER, Energy; Picture 8, ?, BROCK ADAMS, Transportation By Bill Perkins - The Washington Post; Picture 9, PATRICIA ROBERTS HARRIS...changing offices, from HUD to HEW; Picture 10, Treasury Secretary Blumenthal and daughter Ann Vollman after his dismissal. By James M. Thresher - The Washington Post