[Barnacle Bill]

A mine in space would not work like an old-fashioned naval mine, exploding when something hit it. Space being vast, the chances that something will run over your mine is remote. Even with a proximity fuse, the warhead would have to be huge to cause any damage at all. So, for mines to be realistic in space, they would have to be one of two things:

1) A stealthed seeker that waited to activate until it detected a target in range. Some modern naval mines are this already.

2) A disposable (bomb-pumped) one shot non-seeking weapon that fired at the first target which came in range (or perhaps held fire once the target is in range until the range to target starts increasing).

In scenario 1, point defense would work and you'd need a bunch of them to be effective (enough to saturate PD).

In scenario 2, you could postulate that the bomb-pumping the weapon makes it more powerful than even massive base-mounted weapons. You'd avoid having to play out the interaction with PD. However, it could still miss and the target's ECM would help it miss (you'd need to add combat sensors in your mine design).

In either scenario, you'd have the possibility of ships coming through the sector without getting within range. Again, space being vast, the chance of a ship coming within range of even one mine as it passed through the minefield sector would be remote. The only way to deal with that is to make mines a warp point-only weapon which attacks only enemy ships using the warp point (either direction). Then you can postulate the mines are all set up within range of the warp point. Note that this does not save the concept of a simple explosive mine. If they were all close enough to the warp point to damage something coming through, the first mine that went off would either detonate or destroy all the rest. They'd all have to go off together, probably over-killing the first target and letting the rest of the enemy fleet come through unharmed.

Using the warp point-only idea in combination with scenario #2 would make mines work more or less like they do now, in warp point sectors. However, you'd still need to address the interaction between the mine's fire control system (scanners, combat sensors, etc..) and the target's passive defenses (ECM, cloak, etc...). Cloaked ships that could not be detected by the systems installed in the mines would simply not set off any mines.

So, what is mine sweeping in that case? Probably some sort of very short-ranged decoy that goes through the warp point first to set off the mines.