Solution 1:

The following rephrased sentences remove the of which phrasing but keep the essential meaning. I have tried to also keep a consistent pattern of rephrasing, and I've emphasized the changed words.

  1. But the press cannot expose that of which it is denied knowledge.

    → But the press cannot expose what it is denied knowledge of.

  2. The cause and that of which it is the cause go together.

    → The cause and what it is the cause of go together.

Solution 2:

"But the press cannot expose that of which it is denied knowledge."

That of which it is denied knowledge --> what it does not (or cannot) know.

But the press cannot expose what it does not (or cannot) know.

"The cause and that of which it is the cause go together."

That of which it is the cause --> its effects

"The cause and its effects go together."