These type of mercenaries have as favorite target: Defensive Buildings. So their main mission is to first go attack and destroy all the defensive towers that are present in a city. They have high hp, low attack damage and moderate movement speed, they will always attack the defensive towers until all are destroyed, when all the towers are destroyed they will attack the next closest building.
Only Pharaoh Warrior is different from the group with their low hp and high attack damage, their role is to support the main tanks in higher levels when the towers are fully Fortified and it takes a lot more time to take down due to the 50% damage reduction that the fortification have..
The Siege Tower was introduced as a reward of the Plague Warriors event. This Siege Tower also has "Favorite Target:Defensive Buildings" and can also be considered as a Tower Destroyer even though it not a mercenary but a tower.
The Cyclops was introduced as a reward of the Pumpkin Warriors event. The Cyclops also has "Favorite Target:Defensive Buildings" difference between other tower destroyers is that the Cyclops is the only one with splash damage.
With the 2013-07-26 update the Mightosour also became a Tower Destroyer when it reaches level 6. His behavior was changed from "favorite target: non-utility" to "favorite target: Defensive Buildings".
With the 2014-08-04 update the Favorite Target of the Persian Sapper has been changed from Anything to Defensive buildings. Making it the fastest moving tower destroyer and also has the ability to avoid all damage from towers while being underground.