Some of the most dramatic moments in stories are abruptly halted, cut off in the middle. When the rest of the scene is finally revealed later in the story, it's pretty heady stuff. Cutting away can be a great writing technique to make any story more thrilling. But it can also be done too much, and poorly, in ways that will simply wreck your story.
"There is no more need for questions, Inspector." The interruption halted the room, and all eyes turned to him. "I believe I know who killed Mr. Monroe."
Two weeks before that fateful night, Phillip was in Tangier...
Cutting away from a scene at a pivotal moment has a number of different effects on a reader. It heightens the tension and draws out the suspense of the story, certainly, but it's also frustrating. When a reader is caught up in a scene and they feel themselves edging close to a conclusion that isn't delivered, it can be incredibly annoying.
The secret of great writing is annoying your readers just enough to keep them reading. Cross the line and you'll alienate them. Readers give up on writers quickly, and for lots of reasons. If you fail to deliver, they have every right to put your book aside. The trick is to continue to make the reader bend, and bend, without breaking them.
The crux of it is that you have to finish the scene, and don't wait too long about doing it. If you cut away from an important scene and then come back to it later, you have to make it satisfying. Be sure the scene delivers vital information to reward the reader for their patience. Do it well, and they'll reward you by continuing to read your work.