Do you understand that by their very nature, underwater cables have to span the width of a body of water? What are you going to do, draw a line of mines from Denmark to Sweden?
Make passageways or even deactivate mines using signal from the same cable it is safeguarding. Ship needs to pass, captain sends an SMS from a sat and the mine is deactivated for half an hour. If ship is suspicious, a destroyer escorts at at gunpoint - cable signal lost, torpedo goes off automatically.
Great idea. I was thinking of something similar after 9/11. Install explosives on all commercial airliners and have them automatically detonate and destroy the plane if it gets too close to a building where it isn't supposed to be. It's foolproof!