If i have to fight minelayers, the fast nifty ones, i usually fly at low speed, and when they come from the aft or flank, or even head-on i HET and tractor them with a lvl 4 or 5 or of course tractor them and then HET. Then it is my turn to be bad. Usually they don't survive it. Just put your ship in full reverse to be sure that you don't get hit by them. AM-mines are fine to me though. Just make sure there are not two ships with them on your map.
Aenigma