Usually when you ask contractors to save the materials they would be more careful in try to keep the demolished parts as reusable as possible.

Living as we do in the Bay Area, many contractors are using green concepts to further their business model. Green building is actually mandatory in CA for new construction and is being phased in for remodeling in the next five years. Reduce, re-use, recycle. The mirror may not survive it's removal but all else could be donated to the local Habitat for Humanity Re-Store for a tax credit. Tell your contractor it is to be done and make sure it is in his quote.

@oversier, good for you! :-D

What you want is a "deconstruction" pro, not a demolition one.
Try the Deconstruction Reuse Network
http://www.reusenetwork.org/
For such a small project, they probably won't take it on, but can probably recommend what you can do in your area. Failing that, any competent GC should be able to salvage materials for your reuse, especially if there is a built in contractual reward for doing so (let them take the tax credit) or penalty for failing to (replacement cost of what they break.)

For stuff you want to give away, like Ironwood, we use Re-Store all the time on all our deconstructions.
http://www.habitat.org/restores/

They can be picky though. Glass things tend to get rejected unless in a sturdy frame. Large things that won't fit in a standard home (like 8' doors, etc.) similarly don't get taken. But they'll take most standard cabinets, counters, windows, doors, hardware, electrical and plumbing fixtures (generally not toilets).

That mirror might pop off, and it might not. I would not count on it surviving, and it would not be reasonable to expect any GC to guarantee to be able to salvage it. If it does, great!

Also check out the website of your local chapter of the US Green Building Council. They will have a list of pros.