Question

What evidence does McCarthy provide to support his claims of Communists in the State Department?

Answer 1

To be exactly fair, McCarthy never provided any solid evidence about any of his claims.
In front of the audience, McCarthy only waved a list written on a paper that according to him was the names of state department  employees that were  communists

Answer 2

McCarthy quotes Joseph Stalin as describing an active Communist revolution not being carried out peacefully. McCarthy also names and describes State Department employees such as John Service, Gustavo Duran, and Mary Jane Kenney whom he claims had ties to Communist groups.