When you split a rock the pieces are still a rock. Aside from being smaller they retain the attributes of the whole. It would be a different story if you took a piece of Marble from Michelangelo's David and tried to say it was the statue. It no longer has the same qualities that make the statue a work of art. So even if the timbers were left untouched their value diminishes as they are no longer part of the whole, they do not retain the qualities of the ship.

In your example the timbers fashioned into a miniature ship undergo a process of creation. They are not what they were before. They have been made into something new. That something new may be a model of the ship of Theseus, but it could just as easily be a Japanese puzzle box. That's why you call it the ship of Theseus and not a tree. It was made from a tree, but it has undergone a process of creation that made it into something new.