When you first start chopping, you will feel clumsy, like the knife is not yours. You don’t control it with your strength, you control it by learning what the knife does to the food as you repeat the motion. If you’re just starting out, you tend to push down on the knife, which makes the cuts irregular and the food slip. You’ll have more success by bringing the knife forward and down at the same time, letting the knife edge do the work for you, not your arm. Even an onion can be used to practice rhythm and accuracy.
I think a big mistake a lot of people make is only practicing when they’re preparing a meal. This puts you under time pressure, and when you’re in a rush, you will not use proper technique and will fall back on what you’re used to. So practice separate from preparing a meal. Grab just one carrot or potato, and just practice cutting it properly. Don’t worry about getting dinner ready, just focus on cutting this one thing properly. If your slices are wildly varying in thickness, slow down until each cut feels purposeful. You’re aiming for consistency over speed; consistent cuts mean that the food will cook consistently, and you will be able to tell whether you’re actually controlling the knife or not.
You can have a very useful practice session in under 15 minutes that doesn’t leave you with a pile of wasted, cut up ingredients. Pick a ‘robust’ ingredient (like a carrot or potato), decide that you want to cut it into one type of cut (say, thin slices or small dice), and then cut it. Then, gather up all the cut pieces, and do it again. Either cut the same type of ingredient again, or save the cut ingredients for another time. Listen to the sound of the knife hitting the cutting board. If you hear a smooth, muffled thud, you’re probably using proper technique. If you hear loud banging noises, you’re probably chopping too hard. If the knife gets stuck, don’t force it, just adjust the angle a bit.
If you find yourself getting frustrated, take a hard look at your grip and stance before you decide that it’s just a lack of coordination. If you are holding the knife too far back on the handle, you will not have enough control over it. If you lock your wrist, you won’t be able to make smooth motions. Tucking your fingers up into a fist will help protect them and help you keep the food stable, which will help the knife glide smoothly over it. If the cutting board is slipping around on the counter, put a damp towel under it. This will make it stable, and you will find that your cuts improve dramatically. Sometimes, a better environment can make more of a difference than “trying harder.”
As you get better, you will start to see distinct cuts instead of torn pieces. Your cuts will be generally the same size, your cutting board will remain organized instead of covered in debris, and you will start to feel calm while you’re cutting instead of panicked. And at some point, the knife will stop feeling like something you manipulate, and will start feeling like a direct extension of your hand, something you use to purposefully change the shape of ingredients.