I'm guessing you don't know anything about orbital mechanics. While a satellite can be shifted to a new orbit, this "space mines" idea would be terribly inefficient.
A nuclear powered satellite would not have such a problem. When the space mine uses it's nuclear power supply to increase the effect of the explosion, that explosion would have a large radius. Even if it does not physically cause the destruction of the enemy satellite, it could still fry the electronic circuits of the target to make it dysfunctional.
This just demonstrates that you also don't know much about nuclear detonations in space. A nuclear explosion in space is not that big, most of the energy is radiated as light and heat. The EMP that you are referring to is actually done at high altitude while still in the atmosphere.
Remember, space is BIG. For something to be "close" to be effective, it really needs to be right on top of each other.
On a separate note how does "the space mine uses it's nuclear power supply to increase the effect of the explosion, that explosion would have a large radius" work?? Do you really think having a nuclear reactor near a conventional explosion will trigger a nuclear detonation?? No. it doesn't work like that. At most you'll have a "dirty" explosion meaning that the reactor is destroyed and it's radioactive bits are scattered around.