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Magneto actually attempted this in the comics during the conclusion of the "Fatal Attractions" storyline. He ended up ripping the adamantium out of Wolverine and left him in a near-death state.
BUT, the key thing here is that the adamantium bonded to his skeletal structure isn't his mutant power... his healing factor, heightened senses and bone claws, however, are (though the fact that he started out with bone claws is only relevant in regard to the comics, unless they touch on it in the Wolverine film whenever that sees the light of day).
After the Magneto removed the adamantium from his body, Wolverine's healing factor went into overdrive as it tried to save his life. He ended up recovering but after the fact, he discovered that he had lost a lot of his other abilities (the heightened senses, for example).
It gets more or less convoluted to an annoying degree beyond that (like the revelation that the adamantium was poisoning Wolverine's system and keeping him from fully using his healing factor). To make an already long story even longer, the adamantium was eventually placed back within him by Apocalypse when he was part of one of the many incarnations of Apocalypse's Four Horsemen team (namely Death) during part of "The Twelve" storyline in the comics.
As a sidenote, when Magneto ripped the adamantium out of Wolverine, Professor X was insanely pissed. So much so that he ended up erasing Magneto's mind entirely and putting the poor bastard in a coma. This eventually helped lead into the "Onslaught Saga" event which crossed over into numerous Marvel comics during the summer of 1996.