To quickly expain how a vehicle's Air Conditioning systems works: (I can go into further detail, but I'd rather just give you guys the summary unless you really want me to write a small essay LOL)
The A/C functions on thermal dynamics, heat is generated when you compress a gas, and heat is lost when you expand a gas.
The compressor is designed to cycle on and off, its part of its intended operation, it compresses the refrigerant to high pressure (roughly 100+ psi) and then that compressed gas goes into the evaporator where it expands exponentionally quickly reducing the temperature to near freezing where it is cycled through condenser to once again be pumped through the compressor.
The way the A/C system maintains the lovely frostbitten temperature that you want without freezing itself (and trust me if it didn't cycle the way it is supposed to, you could probably flash freeze beers with how cold it can potentially get... though your evaporator will be frozen by then and a few other things...) is to cycle the compressor on and off to maintain a specified pressure in the system and thus a specified temperature. (as a general rule of thumb, 1 degree of temperature will equal roughly 1 psi in an A/C at rest without the compressor being run)
The A/C is engineered to cycle on and off continiously and it is absolutely normal. Also when you put your A/C into "recirculation mode" it is using the interior air to cool off, thus allowing the A/C to cool off the air quicker, more efficiently, and cooler than it would say if it was 90 degrees outside. If you use recirulation all the time I do, please do yourself a favor and check your cabin air filter and replace it when you need it.