Mew didn't "die" he was "frozen forever"... there was some kind of nervous reaction all of the toys had whenever they ended up getting caught out of the position they were supposed to be in, or they were last left in, and as a result, they become so afraid of being caught to the point they're frozen stiff; it happened to Mew because on their way back to the play room from the living room, Mew accidentally lost grip of Rugby's tail as they raced back to their play room, and he got caught in the hallway when the mother left the bedroom and found him, assuming it wasOuiji the family cat who left it there.
It seems that Christmas spirit, and the love of family and friends is what brought them out of their frozen states, because in the end, not just Mew, but other previously frozen toys such as Ditz the Clown, and a parrot who bears some resemblance to Abelardo, and others awaken.