What did the soviets build in 1961 to cut off allied-controlled west berlin from the rest of germany?

The correct answer is the Berlin Wall.

The Berlin Wall was built in 1961 in order to separate West Berlin, which was controlled by the US, France, and Great Britain, from East Berlin (which was controlled by the Soviet Union). This wall split up families and became a significant piece of symbolism during the Cold War era. This wall symbolized the stark differences between the United States and Soviet Union on how a society should be run, as East and West Berlin were run in two completely different ways.