When I hit "hard acceleration" to pass another auto, my car sputters and cuts out. I have changed everything and had it at the chevy dealer with no results. What could be causing the problem?

This could have something to do with fuel pressure or fuel delivery issues. Replace your fuel filters, fuel pump and fuel pressure regulator (if used). Also drop a bottle of good fuel injector cleaner into your fuel tank. If problem still pursists, I would have your fuel injectors checked out and professionally cleaned. This could also be timing problem. You may look into changing the timing belt/chain as your vehicle is already 10 years old. A worn out timing belt can cause very strange results. A stretched timing chain can do the same. Good luck!