Mines ignore shields.
If you want to clear a mine field then what you need is a fast drone that just speeds through the mine field. It would trigger the mines but won't actually get hit by shrapnel.
But it's far more easier to use PD or better yet Flak to destroy them. The only problem is time and no enemy ship around shooting at you.
As an enemy you can't pass mines without triggering them. They would be useless if you could. Maybe future added features like cloaking or ECM/sensor disruptors could make that possible but not now.
There is another way you could do but takes some time....
it's simpler to wait for them to disappear or fly around