I live in Guangzhou for a while, and my passport is still in visa extension process. I need to go Beijing before I get back my passport. So can I use a copy of my passport to check-in at the airport for the domestic flight?
You'll need some identity document to travel because in China you are obligate to carry at least one identity document with you. See China Idendity Card Wiki
A passport photocopy can be treated as a official document since it be recognized by Chinese officials.
For this you'll need to validate your photocopy in any notary's office or maybe in a Chinese Consulate.
Or as last option you can request in your country consulate a provisory identity document which allows you to flight inside the China.