We were shown Mormont knew Craster was giving children away to the Others. For years. Why did he not tell Eddard Stark? Why was the deserter we've seen beheaded in season 1 called "a madman"?
Mormont would not get involved with Ned Stark's management of his lands and Lord's duties. And at the end of the day, the bottom line is the deserter was beheaded because he ran away from the Night's Watch - so regardless of his reasons, he broke his vows and that's the punishment. I doubt Mormont would plead for the man's life on the premise that "perhaps he's telling the truth" about the Others. It's speculation at that point of the story.
Also, like others have mentioned, its not entirely clear if Mormont knows for a fact its an 'Other' who took the baby. Yes, Mormont has definitely known for years what Craster has done with his sons and admits that to Jon but doesn't state any obvious acknowledgement of what exactly it is that takes the baby - because maybe he doubts it himself yet. He's afraid of it... they're all afraid of it. They know the stories and they've seen the re-animated wights firsthand (hahah HAND, what a pun!). But there's no definite confirmation - yet.