I been wondering... what makes the Earth shake when Mammoth walks and runs?

Well, a quick search of the word 'shake' on the wiki lead me to http://www.creationkit.com/ShakeCamera_-_Game. Not sure if that's what's used to shake it when they walk, but it should achieve the same thing.

Likely a quest script that uses ShakeCamera() when the player is near a mammoth.

The animations do this through annotations calling the function CameraShake.0.3 -> NOT ShakeCamera() the papyrus function it calls a different function specific to animations, of which there are a few available for animators.

alternatively there are also some explosion objects that cause camera shake as well as kicking up dust. you could create a custom explosion with the effects you want.

but if this is for something like mammoth walking where the effect is constantly being called, i'm not sure if placing explosions so often would be a performance-friendly alternative (since it does also calculate physics as well)

Erm, I'm pretty sure that'd be Nirn... Just sayin'.

So i can only remove them if i know how to do animations? im screwed... i am trying to remove that effect from a Mammoth Baby,,,

Editing it out of the animations is fairly easy just use hkxcmd to convert the anims to xml then back to hkx since hkxcmd can not convert the annotations every last one of them are lost but along with losing the Camera Shake you also lose the foot syncing, playsound and other events that are stored as annotations within the animations.

Even if you do that you also need to define a new race using these new animations and set up the animations manager for the new race and create the new actors using the new race.... on and on until completed just to remove that one effect.