Death Adder Hatchling. If you time the Blinding Poison right the Mines will actually miss the ground when they are first cast. Usually an opponent with Mines will cast the Mines first turn and then either switch or try to beat you to the ground - Darkmoon Tonk for example. Other pets with mines like Clockwork Rocket Bots will often first cast Sticky Grenade and then cast Mines. But if your opponent is wise to your Death Adder it will try and wait for the Blinding Poision, so then you might have to postpone the Blind for a turn or two, which of course turns into a chicken race of who blinks first.
Another easy way is to have an elemental in back line. I often just switch them in immediately after mines are down. Elementals takes less damage from mines. Is especially useful with the Jademist Dancer that can heal up almost all mine damage taken. Only downside is that Jademist Dancers attacks are not especially strong vs mechs, though they usually hit hard enough as it is.
Decoy. If you got a pet with this ability you can bring them in first vs the mine-layer. Cast Decoy and you will get 2 stacks. Then you can safely switch pets to remove the mines which will hit the Decoy instead.
There are a couple of pets that has Celestial Blessing, your next pet to switch in takes 50% less damage for 3 turns. I have not actually tested this one out to see if you gain the effect before the damage from the mines.
I guess Murkalot shield will work just fine, but I don't have Murkalot to try it.
Or if you have a nice heal to use after switching in. Like Cauterize, which heals an amount plus half of the damage from the minefield.
If all else fails I try to save a low hp pet in the back line to be ready to switch in and take the hit.
One thing I have noticed is that if I myself use a broom/bone-spider/imp you usually can switch out the minefield pet and at least my opponents almost never switch them back(for quite some time at least). Talk about soft-counter...
