The deepening political crisis in South Africa and President Pieter W. Botha's defiant speech Aug. 15 have stirred universities across the United States to reassess their decade-old resistance to selling stock in U.S. companies that do business in South Africa.

From Harvard to Rutgers to the University of Southern California, institutions of higher education have begun either divesting their South Africa-related stock or reviewing their divestment policies.

At least two dozen schools have sold all or some of their South Africa-related stock since April, with Columbia University here likely to become the first Ivy League school to divest totally when its governing board meets Oct. 7.

What swayed them, according to university officials and analysts, was not the spate of student protests across the country last spring, but the deteriorating situation in South Africa, which has been dramatically televised into American living rooms each night on news programs.

"People have anticipated another round of protests," said Joshua Nessen, student organizer for the American Committee on Africa. "But ultimately, the impetus comes from the situation there."

In making decisions, universities are breaking with their long-stated policy not to allow politics or morality to interfere with fiduciary decisions. On a practical level, according to those monitoring divestments, the schools found that their traditional and often repeated position -- that stock holdings could be used to force companies to work for the betterment of South Africa's blacks -- has become increasingly untenable after Botha's speech essentially slammed the door on immediate political reform.

"One of the most important things to have happened in the last five years was Aug. 15," said Christopher Coons, a research assistant at the Investor Responsibility Research Center, which is preparing an in-depth survey of university divestment activity.

Botha's speech, Coons said, "was what broke the backs of the university trustees; that was what really made the difference."

Wesleyan University President Colin G. Campbell seemed to sum up the erosion of policy when he told The Associated Press that his school believed since 1978 that U.S. firms "can help to eliminate the evils of apartheid." But he added, "The ability of companies to meet this expectation is called into question by events of recent weeks."

Columbia University's move toward divestment illustrates the impact that recent events in South Africa have had. Shifting perceptions have led to bipartisan support on Capitol Hill for punitive sanctions while forcing President Reagan to alter his policy of "constructive engagement" in favor of heightened pressure.

In March, just six months ago, Columbia officials clung steadfastly to their version of constructive engagement as hundreds of students barricaded Hamilton Hall, chained its front doors and refused to leave until the university sold $39 million worth of stock in companies that conduct business in South Africa.

In rejecting total divestment, as the students demanded, Columbia's chief spokesman, Fred Knubel, said university trustees had decided that "the more appropriate and effective policy is to influence the American corporations in which the university holds shares to conduct their business in South Africa in accordance with the broad moral and social ideals of American society."

Then came the South African government's declaration of a state of emergency, daily scenes of violence and Botha's Aug. 15 speech, in which he declared, "We have never given in to outside demands and we are not going to do so. South Africa's problems will be solved by South Africans and not by foreigners."

Less than two weeks after Botha's remarks, a six-member ad hoc committee of Columbia trustees recommended that the school sell its $39 million in South Africa-related stock.

The full 24-member board of trustees is widely expected to follow the committee's recommendation when it meets Oct. 7.

Even Harvard President Derek C. Bok, who has resisted divestment pressures at his Ivy League institution for more than a decade, announced a tightening of his school's South Africa policy last week. Though still rejecting total divestment, Bok announced the sale of $2.8 million worth of stock in two companies, Allis-Chalmers Corp. of Milwaukee and Tokheim Corp. of Fort Wayne, Ind.

"Every thoughtful person has been gripped by the recent events in South Africa," Bok said Thursday.

"The widespread violence, the mass arrests following the declaration of a state of emergency and the stubborn refusal of the Botha government to extend full political rights to the black South African majority have deeply troubled individuals and institutions everywhere and made them consider how they should respond to such cruelty and repression," he said.

Other divestment actions include:

*Total divestment of South Africa-related stock by Arizona State University, California State University at Northridge, Barnard College, the University of Iowa, Stony Brook Foundation, the University of Massachusetts at Amherst and Ohio State University.

*A joint committee for Rutgers University's two governing boards recommended divesting $7.5 million in stock "as soon as prudently possible;" one board ratified the decision last week, and the other was expected to do so within two weeks.

*At Princeton University, a special committee is reviewing $345 million worth of South Africa-related investments. "The events during the summer have inevitably affected the members who are reviewing the policy," said university general counsel Thomas Wright.

*Fifteen other schools have partially divested since spring, the largest being Grinnell College in Iowa, which sold $9 million worth of South Africa-related stock, followed by the State University of New York system, which sold $4 million worth of stock.