Mook Doors are spawning points for Basic Mooks and Suicide Bomber Mooks. They are mostly encountered in jungle-themed levels and will keep spawning mooks until destroyed.
The best way and the only way to exterminate a Mook Door is to destroy the ground underneath. It will kill every mook coming out and ultimately result in the Door's destruction.
It is best advised not to stay close to such a door after destroying the ground it rests on, since the Suicide Bomber Mooks falling out will immediately explode and can kill the player. The door itself also create a massive explosion upon destruction so do it with ranged attacks.