Hello!
The A/C clutch is engaging because the A/C compressor operates when the heater is in the "defrost" position. The defroster air is chilled to remove any moisture (remember the dripping condensate under the car in the summer?) and is then passed through the heater core to warm it before it blows on the windshield. Refrigerating the air to remove moisture prevents the windshield from fogging up when the defroster is on.
The description of the problem is consistent with a failed AC compressor. When the compressor clutch engages, it is putting a heavy load on the belt, and a large electrical load on the charging system. The compessor should have some resistance, but should easily be able to be turned by hand. With the engine off, grab the front of the clutch (the part that is attached to the compressor shaft) and see if it turns fairly easily. If it does not, the compressor has internal damage and will need to be replaced.
The clutch cycles in and out fairly often because the system is probably low on refrigerant. There is a pressure switch that shuts the compressor off when low side pressure drops below a certain value; the compressor cycles because there is still some refrigerant in the system, but when the compressor turns on momentarily it drops the low side pressure below the cutout point almost immediately. the result is that the compressor will continually try to cycle on and off pretty quickly.
Allowing an A/C system to operate while it is low on refrigerant is probably what damaged the compressor; the refrigerant circulates lubricant and if refrigerant level drops low due to a small leak that is not corrected, teh compressor operates without lubrication. Over a long period of time, the result is a failed compressor.
This is not the type of repair you can perform at home in the driveway; special equipment is needed to evacuate the refrigerant, clean the debris from the rest of the system, and to vacuum all of the air out, recharge it and check operation. This is a job for your favorite local repair shop...
In teh meantime, if you unplug the electrical plug at the compressor clutch, it will stop the compressor from engaging and allow you to drive the vehicle untill the AC system is repaired.
I hope this is helpful; if so, an accept would be most appreciated! Thanks!