I have Craftsman 22'' 179cc snow thrower. The auger does work but the blade catches some snow it it stop working.

Is it still under warranty? If so, take it back to the Sears store to be repaired.
If it's way passed the warranty, is your gas new or has it been in the tank for months? Premium gas is the best for 2-cycle, 4-cycle engines. It doesn't gum up the carburator. Regular gas, in the past 10 years, isn't very good quality, and according to my repair person, will gum up the engine. He is right! I have been using Premium for 3 years now, with no problems, in 2 riding mowers, and a Husky weedeater, and a chainsaw.
With the demand for more power, pushing out the snow, the carburator could be clogged up with gum deposits, if you have been using regular gas for an some months. Good luck.