The cost savings here in relation to the overall project amount is not significant enough to weigh out the risk of doing it yourself. You might save a couple of thousand dollars but there is a lot more to it than you might think.
Disconnecting plumbing and electrical, protecting your home from dust and debris, carrying heavy appliances and countertops through your home and out the door are just a few things to concider before tackling the demo on your own. Even then, once everything is out how will you dispose of it? I would always reccomend having the contractor performing the work to perform the demo.