Moving to decentralize the management of already widely scattered cable television systems, Warner Amex Cable Communications Inc. announced a major reorganization today that includes eliminating more than a fifth of its corporate staff.

The moves, which included dismissal of at least four Warner Amex vice presidents, represent the first major steps by Drew Lewis, the former Reagan administration Transportation secretary, to streamline the cable venture and move it toward profitability. Lewis took over the cable concern Feb. 1.

"I am convinced that in this business you need broad-based people out in the field," Lewis said in an interview. "If we don't have somebody to run Timbuktu, we'll hire people there to do it."

Lewis said there had been "a lot of tensions within the organization" between company headquarters and field staffs, such as in the marketing area. "What it really means is that I want to start operating the cities out of that base instead of out of New York," Lewis said.

The announcements today included word that 57 of the 274 corporate staff jobs here had been eliminated and that the firm's programming, marketing and sales operations had been temporarily consolidated under Richard Aurelio, who had been in charge of government affairs.

In a letter to employes, Lewis said the company's focus "would no longer be centered on franchising but achieving profitability."

Asked about the company's financial picture, Lewis refused to offer specific predictions, but said it is "clear that the company will be profitable."

He did say, however, that Warner Amex officials are for the first time considering financing the construction of recently awarded franchises through limited partnerships rather than from the capital investments of the two parent companies, Warner Communications Inc. and American Express Co.