In Mayhem, you must do a certain cost of property damage before time runs out. The destruction is great fun but can get hard very fast if not played right, you get weapons that have unlimited ammo at different times, mostly SMG's and pistols have that effect and the weapon itself would change as well without the player choosing. A bonus effect is given from time to time either as a use a weapon bonus or destroy a certain car bonus, as well as for destroying various furniture in the specific area in which you are assigned to.
This activity has an area limit, but destroying things outside the zone is still counted as long as you are still in the radius of the area. Your wanted level will increase, but will be removed after exiting the activity. Combos are used to increase the amount you get from destroying items. There is a timer for combos, but it is increases when more points are earned.
Note that the timer stops when you are outside of the area, and that collision rules apply. (If it won't get knocked over/down by driving your vehicle into it, don't drive into it.) You can combo and gain more money per destruction, which you will eventually need; an easy way to do this is to line up a car with the long axis of a line of wire fences and then just drive straight forward, hitting them in quick succession, one right after the other.
When driving, your car has more durability and far more superior strength than all the other cars on the road, it will not destroy cars on impact but launch them into the air a mighty distance.
The best strategy is to simply take a Bulldozer (one should be parked right next to your Saints Row Loft, near the construction site). Drive to the Mayhem area, and then just run anything that's linked, such as a chainlink fence over and anyone that gets in the way. Since the Bulldozer is already extremely tough and police don't pull you out, you can pass at least two levels before needing to get a new one.
Finishing Insurance Fraud beforehand helps a lot because of the infinite sprint reward.
Just as in the previous game, street furniture is the key to finishing Mayhem because there are ways to destroy a lot if it in a short amount of time to get big combo bonuses.
From the areas you are send to, Hotels & Marina and Chinatown are the easiest places to find big clusters of street furniture. Look for shops that have tables, chairs and umbrellas outside or find the market stalls, benches, fences or lamp posts.
The best strategy of beating the Mayhem is simply to bring a Challenger or Crusader into the icon, start the Mayhem, and turn the Mayhem into Tank Mayhem instead. However, due to lack of vehicle targets, and lack of health pickups (Wrench Icon), this one is harder due to the fact causing destruction with the tank is the quickest way of gaining notoriety.
Mayhem was removed from the Japanese version of Saints Row 2, along with Hitman and Human Shield.
Since one of the major complaints of Mayhem in Saints Row 2 was that sessions often turned into long sessions of blowing up fences, The Third makes fun of this constantly - the first Mayhem mission in the story has Kinzie assigning the Boss to blowing up a fencing company (as in the barriers, not the dealing of stolen goods) that was serving as a Decker front, and the Achievement/Trophy for all the Mayhem missions is "Fence Killa 2011".
Mayhem is not included in the German version of the game.