2low , If I understand what you are trying to say is ; the 2 - 220V 15amp circuits in your breaker box will not be energized if you turn ONE of the TWO 220V 15amp breakers OFF , neither circuit will work . CORRECT????
Before proceeding IF YOU ARE UNCOMFORTABLE WORKING IN THE BREAKER PANEL HIRE AN ELECTRICIAN !!!
If that is correct than you have bigger problems in the box !! Now before you do anything in the box shut the Main breaker for the box off , remember the main power coming into the box will STILL be HOT (live current) . It sounds as if you have some wires crossed in the box . Making for a very dangerous situation as with one breaker feeding one leg of the 220 circuit and the other breaker feeding the other leg of the circuit , you could still have power on one leg of each circuit when you had thought the power was turned off .
Once the Main Breaker is off trace the wires feeding the circuits from the breaker out through the side of the panel , see if both wires from the one of the breakers go to the same circuit , if one goes to one circuit and the other goes to the other circuit you have just found the problem . You can fix this problem by changing the offending wire over to the correct breaker for that circuit . Remember to retrace the wires and make sure they are running to the correct breakers before turning the power back on .
Disclaimer , this advice was freely given and is worth what you paid for it , as I am NOT an electrician , I accept no responsibility for anything that could possibly happen from the use of said advice .
Be careful and read and heed all warnings before proceeding .

Dan