The picture illustrates what happens when the old growth is not cut back. Notice how the new green growth has grown up into the old. Now it’s very difficult (if not impossible) to cut out the old growth and not damage the new.
I happen to like the straw-like look of the ornamental grasses during the winter and therefore, leave them standing. Some folks don’t like that look or are just indifferent and they may choose to just cut them down during the fall clean-up process.
Whatever your choice might be, there are a few ways to cut them and this might depend on the type of ornamental grasses and what condition they’re in. For example, is the old growth dry & brittle or soft & pliable? I find it best to be prepared with a few of the tools I mention so you can experiment for the most effective one.
I’ll even use my bypass hand pruner in a pinch and that works fine if you grab a bunch of strands with one hand and cut with the other. This is the method I used to “prune-out” the old, brown growth from the new growth in the first picture.
Always remember a dull tool is hard to work with and very dangerous. Of course you must be equally careful with a sharp tool, but sharp tools will do the task with predictability. Just keep your eye on the cutting part of the tool at all times.