A Pershing II test missile began to break apart 70 seconds after launch yesterday from Cape Canaveral and was destroyed by the range safety officer, according to an Army spokesman.

It was the third mishap in the last four tests of the nuclear-tipped ballistic missile, which is designed to hit targets inside the Soviet Union from bases in West Germany.

Deployment of the first nine of a planned 108 Pershings is scheduled to begin in West Germany in mid-December, along with the beginning of deployment of U.S. ground-launched cruise missiles in England and Italy. The cruise missile, also still being developed, completed a successful test flight yesterday, Pentagon officials said.

Although two flight tests are left in the Pershing II development program, initial production models have been delivered to the Army, according to a spokesman for the Martin Marietta Corp., which is building the missile.

"Several units were delivered in May," he said, "and others are in production."

Because it could reach targets in the Soviet Union from its West German bases in less than 10 minutes, the Pershing has been considered by NATO countries as the major bargaining chip in negotiations with the Soviet Union at Geneva to limit the number of medium-range nuclear missiles in Europe.

Deployment of the two new American missiles was approved by the alliance in 1979 to offset continuing deployment by the Soviet Union of its new SS20 medium-range missiles targeted on western Europe. Moscow has vociferously protested the planned deployment of the new U.S. missiles and threatened to respond by placing more nuclear weapons in east European countries.

Martin Marietta officials said yesterday that it is too early to say what caused the missile to malfunction. The trouble occurred six seconds after the second-stage engine ignited. At that time, a spokesman said, pieces of the missile broke off and the range safety officer destroyed it.

Four of the 16 Pershing II flights tests have been described by the Army as failures, including the first shot, which exploded 17 seconds after launch. A fifth test, an official added, achieved its primary flight distance goal early in the test program, but failed to meet its secondary goal of hitting the target.

The 13th shot at White Sands Missile Range in New Mexico on June 19 failed when the warhead went out of control and fell short of its target. Earlier this month another White Sands shot ended when a safety device, used just for the test, sparked and short-circuited the computer in the warhead, keeping it from directing guidance to the target.

One official said last night that he believed yesterday's problem would be identified by today. He added that "like the last two, I think it will be corrected quickly."

If it turns out to be more serious, he said, it could mean that changes would have to be made in the Pershing units already in the hands of the Army.

The concurrent testing and building program for the Pershing was adopted so that the first nine missiles could meet the December deployment date. Any delay, according to NATO officials, even for technical problems, could create increased political tension.