Seek Remnants
The amount of variety will be limited, but the savings could be well worth it; by choosing a remnant, you could save anywhere from 10% - 90% off the price of a slab.
Donate Trash
Anything you were able to salvage from your demo may be saved and desired for resale by Habitat for Humanity in one of their ReStores. Find out more here.
Demo Yourself
Got a sledgehammer and a reciprocating saw? Now all you need to do is order a waste container from a demolition company and start swinging! Be sure to not take out any load-bearing walls, and don't cut any
live wires. If the risks seem to high, then you may want to hire a professional.
Start Off-Season
First of all, you'll keep your contractor happy by keeping them busy when they're usually slow. Make sure you find out if the contractor is willing to give you a discount for starting late (before or after winter holiday).
Finish on Your Own
Doing things like caulking (if you're good), attaching kitchen hardware, or other finishing work can save you a bunch of money - The cost of having a whole crew on-site doing finishing work can add up quickly.