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.
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.
Use "Barrel Behind the Door" and "Spell of Pain" to deal to your opponent the damage you would have taken by this card's effect, note that this card's effect can deal almost 2000 damage per combo.