That's my primary writing advice.
My writing style in No Greater Love Than This has been described as "haunting," "sparse," "brutal." That's on purpose.
If you want to write a similar way, here's how:
Cut it. Cut it until there's barely anything left. Until you can't cut anything else. Then, add back in where you need to.
This isn't chipping away at marble. If you go too far, you can reverse it. Once it's gone, it's not gone forever.
Keep a separate version, if you must. The big one, the bloated one. But cut away until the only thing that's left is your story.
Get rid of those adverbs, and that sentence that says the same thing as the one before it.
You probably won't even want to add anything back in, when you're finished. Because you never needed it anyway.
Just cut, cut, cut.