1. "Play Game" clearing. In order to avoid taking too much damage from CD's and scouts so you don't have to spend turns UNOing you usually want to walk into the mines rather than clicking "Attack".
To avoid spending turns walking in and out of sectors you can instead click play game when you have entered the sector you want to clear. Then you lose your green sector and will only have to spend 3 turns for the next attack instead of 5. Just make sure you end up having a green sector to safety on your last attack so you can get out the right way when you're low on defense.
2. Full clearing. Don't just kill the mines but kill all the forces. That way you force the mining alliance to get new seeds from everybody or to live with less stacks in the future.
Those were my ten cents. Note that this is the most effective strategy I know, not the most safe
), LB and Phoenix