How do you stop negative thoughts? You plant good thoughts!
When you try to stop negative thoughts, you are focusing on what you don't want - negative thoughts - and you will attract an abundance of them. They can never disappear if you are focused on them. The "stop" part is irrelevant - the negative thoughts are your focus. It doesn't matter if you are trying to stop negative thoughts or control them or push them away, the result is the same. Your focus is on negative thoughts, and by the law of attraction you are inviting more of them to you.
The truth is always simple and it is always easy. To stop negative thoughts, just plant good thoughts! Deliberately plant good thoughts! You plant good thoughts by making it a daily practice to appreciate all the things in your day. Appreciate your health, your car, your home, your family, your job, your friends, your surroundings, your meals, your pets, and the magnificent beauty of the day. Compliment, praise, and give thanks to all things. Every time you say "Thank you" it is a good thought! As you plant more and more good thoughts, the negative thoughts will be wiped out. Why? Because your focus is on good thoughts, and what you focus on you attract.
So don't give any attention to negative thoughts. Don't worry about them. If any come, make light of them, shrug them off, and let them be your reminder to deliberately think more good thoughts now.
The more good thoughts you can plant in a day, the faster your life will be utterly transformed into all good. If you spend only one day speaking of good things and saying "Thank you" at every single opportunity, you will not believe your tomorrow. Deliberately thinking good thoughts is exactly like planting seeds. As you think good thoughts you are planting good seeds inside you, and the Universe will transform those seeds into a garden of paradise. How will the garden of paradise appear? As your life!