This sounds like you may have a faulty Coolant Level Sensor. When this sensor is faulty, it will read an incorrect "low" level, and trigger the light/warning alarm. It is located near the top of the radiator.
The sensor itself is a piece of cake to change. I really wouldn't recommend cutting any wires that kill the buzzer/light seeing as if you fix the "actual" problem, the system will function correctly in the future, just in case you actually DO run low on coolant. Running out of coolant can be the death of a motor, and you really do want to be informaed of that. I suggest changing the sensor (which should be available at any local parts store) and do the job correctly.