What is a small tusked mammal called?

There's no single word for a small tusked mammal, as many different animals fit that description. To give you a more specific answer, I need more information.

Tell me:

* What kind of tusks are you thinking of? Are they made of ivory, bone, or something else?

* What size are you picturing? Is it a tiny creature, like a shrew, or a larger animal like a wild pig?

* What kind of environment does this animal live in? Is it a rainforest, a desert, or a grassland?

Once I have more information, I can give you a better answer!