Trying to bypass it by just removing the belt from the compressor pulley will likely lead to:
* Belt slippage: The belt won't have enough tension to properly drive the alternator, power steering pump, and other components. This will cause inconsistent power and potential damage to those components.
* Further damage: A seized compressor can damage the belt tensioner or other parts of the system.
The best and safest solution is to replace the A/C compressor. While it might seem like a hassle, running the car without a properly functioning system is more likely to result in more expensive repairs down the line. Trying to jury-rig a bypass is not recommended.