Change motion of the animator state

I have many animations in my project for a single character. Instead of creating dozens of clips with different motions each, is it possible to simply switch the motion of the animator state without creating new ones?

Take a look at the image below. I would simply want to change the "AnimationClip1" with "AnimationClip2" through a script.

 

You need to create an Animation Override Controller, and set it to this controller.
Also setup your Animator to the Override Controller instead.

If you don't need to do it in runtime, you can assign animations there.
Otherwise, do as in manual:
https://docs.unity3d.com/ScriptReference/AnimatorOverrideController.html