The above event is also known as the Cuban Missile crisis, which occured in 1962.
The reason why US cut the tie:
1) Castro wanted to built a communist government with USSR’s back which was against US’s Ideology of captialism.
2) USSR implanted missiles in Cuba after Castro overthrown the original government to replace it with communist government. This greatly threaten US’s safety as Cuba is very close to the Western Europe and US.
Therefore ties were cut between Cuba and US.
Hope it helps!
