"It will stop raining soon."
Translation:Vai parar de chover logo.
Yes, but it depends on what you mean. "Deixar de fazer" is usually a more long-lasting action, more like "Quit doing". "Quit smoking!" = "Deixe de fumar!"
You would not usually say "Eu deixei de correr" when you simply want to say "I stopped running", unless you mean you won't do it again in the near future.
But "deixar de fazer" can also mean not to do something you want to do, because you have to do something else instead.
For example, "I didn't watch my favorite TV show because I had to help my father" = "Eu deixei de assistir meu programa favorito para ajudar meu pai".
The literal meaning of "deixar" is "leave" and in this last example it means you had to "leave" something because you had to do something else instead (and you're not so happy about it).