I used to be horrifically verbose. Something most people could explain in one or two sentences would grow to three or four paragraphs!
I'm not always perfect with it now. I still sometimes end up writing a novel when I meant to write a poem. But I have improved exponentially. And what worked for me was getting a job that required me to discuss the most pertinent points of a topic, my opinion, and crack a joke or two all in 150 words.
I'm not suggesting there's a job like that to be had out there, or that you even have to search for one to cut back on your wordiness. But maybe a writing exercise would work. Pick a topic, set a small word limit and try to cover as many pertinent points as possible without going over your limit. Start with a narrow, focused topic like your favorite cartoon character (for example) and then the next time you write, broaden your scope to the other characters in that particular show. From there, move on to the characters that production company works with.
I just came up with this off the top of my head so who knows if it'll work. But it's worth a shot!
Also, the cartoon characters topic is just a suggestion. Pick anything! Sex toys, trees, clothing brands, your favorite musician, etc.