This card can be searched by Single Purchase, Temple of the Kings, Transmodify, "Rescue Ferret", Goblin Zombie, Pyramid Turtle, "Samurai Skull", Soul Rope, Resonator Engine, Vampire Dragon, Summoner Monk, Dragunity Corsesca, BOXer, and Frontline Observer.
In case "Zombie Mammoth" does get destroyed, you can avoid Effect Damage if you have Des Wombat on the field.
If "Zombie Mammoth" has been added from your Deck to your hand OR Special Summoned by the effect of "Goblin Zombie" or "Pyramid Turtle" respectively, you can have "Zombie Mammoth" on the field without fear of not having a Zombie-type monster in your Graveyard.
* If you have a monster in your Graveyard but it's not a Zombie-type monster you can use Zombie World to change it to Zombie.
Change this face-up monster to Defense Position and use Creature Swap or Shien's Spy to give it to your opponent, then attack it with a monster with Piercing-attack. You will inflict high "Battle Damage" (since it's DEF is 0) and 1900 Effect Damage to your opponent.
Giving this card to your opponent will most likely cause it to be destroyed by it's own effect unless your opponent has Zombies in their Graveyard. If they do have Zombies in their Graveyard, you can steal them with Il Blud, Zombie Master or Doomkaiser Dragon.
If you have a face-up Skill Drain you can negate "Zombie Mammoth" effect and have a normal 1900 ATK creature on the field.
Giving this card to your opponent by means of Creature Swap is a great way to inflict a quick 1900 damage, and have the card returned to your own graveyard to special summon later.