In 2009 Fox brought the origins of Wolverine to the big screen, though the movie was mediocre at best, the lowest point of the film was when Deadpool made his first appearance and became the worst screw up in Comic Book history. The movie introduced Wade Wilson, Deadpool, The Merc With A Mouth, but in this instance The Merc Without A Mouth. That very reason is why the first incarnation of Deadpool is in fact the worst thing to ever happen to a Comic Book character in a movie — thankfully Fox corrected their error with the recent Deadpool movie.
Today, Alec and Tom from studioADI, the creators behind the Deadpool in X-Men Origins: Wolverine explain why The Merc With A Mouth had no mouth. The two go one to explain just how little control they had over the creation process even though they were in fact the creators. Alec talks about all the politics that were taking place Marvel, Fox and they respective lawyers. He also says the reason for Deadpool not having a mouth was because he was taken out of the recreation process a bit early.
You can skip to 3 minute mark to see the explanation in full.