Don't cut up his food. In the wild they keep their beaks trimmed by biting. They have to bite off the plant from the stem, etc. And occasionally in the wild they will 'sharpen' their beak by rubbing back and forth over a rough rock.
You can also help wear t down by using some slate, or some other sort of flat rock, to put your food on. While your tortoise eats, it will hopefully wear down.