By far the easiest method to kill Krampus is to simply put it to sleep (Sleep Dart, Pan Flute). Then kill the Krampus with a Spear or Tentacle Spike.
Alternately, the player may kill Krampus in direct combat. This can be done by first using ranged weapons such as a Boomerang or a Blow Dart to strike Krampus, which will cause Krampus to engage the player. Then the player may lure Krampus into hazards such as Tooth Traps.
If the player keeps track of their "naughtiness", they can set a trap for the Krampus before its arrival. The player should place a Chest with a few dummy items between where they will do the final act. Then the player should surround it with Bee Mines. The Krampus should go to the Chest, trigger the mines, and die from the bees. A player without traps or mines can directly engage Krampus while it's busy with the chest.

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Krampus takes 3 blasts from the Ice Staff to be frozen.

With normal damage modifier characters, Krampus takes 6 hits with a Spear; 5 with a Bat Bat; 4 with a Tentacle Spike, Ham Bat, and Thulecite Club; and 3 with a Dark Sword to be killed.

Another way to farm Krampus is to kill Rabbits with Traps, and when the loud hissing sound is played, get a Rabbit, go away from the camp, place a random item or two on the ground and kill the Rabbit. As Krampus spawns, it will take away the items. If the player fails to kill Krampus when it is taking the item, drop another one, though Krampus may have disappeared already.
One of the funniest ways to kill Krampus is by putting a small stack of killer bees into a remote chest, and then letting it destroy the chest, setting off the bees.
A good way to get items back is to make Krampus run into some Frogs: their tongues will make Krampus drop its stolen items, which can be picked up at will.
If the player is aiming to get Krampus' Sack, try using the Fire Staff since the sack doesn't burn. Krampus' other drops will be turned to ash, but since they are common drops, this isn't a big deal.

Krampus will break Chests, then proceed to steal everything before retreating. Krampus will also pick up items lying on the ground prior to destroying chests. In order to get their items back, players must kill it and pick up the items. Krampus will not steal the Eye Bone, Lucy the Axe, Willow's Lighter, Abigail's Flower, Pile o' Balloons, Codex Umbra, Wooden Thing components (Ring Thing, Crank Thing, Box Thing, and Metal Potato Thing), and Divining Rod.

Krampus moves fairly fast, dealing 50 points of damage per hit to unarmored targets, which can kill most characters in three hits. Krampus has a 1% chance of dropping its item sack upon death, which can be equipped like a Backpack. It yields 14 inventory slots rather than the Backpack's 8, and it doesn't slow the character like the Piggyback.

When killed, Krampus will drop all the goods he stole along with one Monster Meat and two pieces of Charcoal. Krampus also behaves similarly to a Gobbler when being pursued. He will disappear into his sack if the player doesn't kill him fast enough.

Krampus will keep running around the player until no more items exist on-screen.