The tank not tanking should have 0 problem getting 2 of the 3 mines each set. The third mine can be iffy; if they are too spread out, he can struggle to physically get to the mine(but should be fine handling the damage). They should make the call each mine set if they can get it or not, if they can get all 3 thats awesome. To note, if two mines are really close to each other you can hop on one mine and before it knocks you into the air, hop onto a second, cutting down time spent flying around.
Of your DPS, Hunter Deter can be used to soak 1 mine, your warlock can either spec dark bargain to soak a mine, or use unending resolve+last stand to survive(various combinations of warlock cooldowns work to soak). Your Holy Paladin can also soak with Bubble, and he can also make any other person soak with HoPo. If he specs clemency he'll have two Hopos to soak with, but overall less soaking through the fight, Unbreakable Spirit will let him soak every 2.5 minutes. Your MW should be able to soak with Dampen Harm specced. If your ele has a shield equipped, he can soak with Astral Shift specced and Shamanistic Rage used together. Your mage can theoretically soak with Ice Block(gotta be quick though) and Greater Invis.