My Craftsman smowblower starts fine, but whe I pull the handle back to start the auger it makes a screaching break sound and kills the motor.

Basic possibility's. I don't know what you have in a safety switch. Here's what to look for. Safety switches operates in two basic ways. The electrical safety switch will stop the spark going to the spark plugs and shut down the engine.

The other is Electoral with mechanical This is an electrical safety switch that operates a solenoid that in turn operates a mechanical brake/stop that won't let the pulley/chain drive run free and dog down the engine and shut off. The other possibility is a bearing(s) are rusted or shot on the pulley belt/chain gear and stop will stop the motor also. This will cause the motor to shut down because of load. Put your snow blower in neutral Engine OFF then check your pulley/ chain sprocket and see if it spins easily and the bearings on the shaft are in good shape and not a bad or broken bearing. Bearings are really sealed by metal caps and on a lot of snow blowers and rototillers press sealed into the actual metal frame of the machine. It sounds like you have a pulley belt driven setup. Check for broken belt jammed between the pulley and the machine frame or cover. Check any Idler pulleys that might be in the configuring to transfer energy to the auger . Use a wire brush for rusted areas and WD 40 or liquid wrench to free up things if that what the problems is. Iam betting on bearing or belt being stop because it being broken or out of sink. With another pulley Also check self propelled system to the wheels. Check the handle Mechanism and if catching or moving properly down in the machine if its Mechanical. One last thought . Look under the handle and see if there's a contact switch that the Handel depresses when you grab it. Something there might be bent. Out of adjustment. Or not depressing properly or bad rusty contacts in the switch

If it's a briggs and Stratton engine, there is the possibility that the clutch under the blower housing is bad. It can be cleaned, but watch the 5 balls or so. Otherwise it will cost you about $15.00. It's a high RPM screeches. Random in nature.