Hello!

The question is broad as animations (Mixamo or not) can be added to Animaze in many ways, most of them involving the Animaze Editor (that is usually where animations are added and removed in an itemized fashion).

I will go ahead and assume you are specifically referring to just the fast lane, Mixamo direct-to-app import pipeline, meant for more casual use, that avoids the Animaze Editor altogether.
Let me know if that is not the case.

Currently, on that pipeline, there is no easy, direct way of deleting a specific imported animation via the UI.
You can do so by diving into the program files, but you do need to be a bit of a modder to do so.



Method 1 (technically simpler) is a full reset and re-import:
If you still have your original downloaded FBX files of the animations you want to keep, then you can
a. reset the Mixamo imports folder in Animaze back to its default state, by deleting its folder completely,
[AnimazeInstallFolder]\Data\Resources\AvatarMixamo\
then getting its default state from the server with "Verify integrity of software files" on Steam.
b. re-import only the FBX animation you want
and you're done.
From that moment on, before importing a new animation (that you are unsure about), you can back up the contents of your [AnimazeInstallFolder]\Data\Resources\AvatarMixamo\ folder somewhere, so you can always restore that state.



Method 2:
This should not be attempted unless you are an experienced modder, breezing through editing script files, and are not afraid to break things and re-set them to how they were before from back-ups that you have set-up beforehand.

It involves manually editing the contents of the
[AnimazeInstallFolder]\Data\Resources\AvatarMixamo\Animations\ folder and also editing the
AvatarMixamo.citem file, in a text editor if you are old-school, and removing the entries you do not want from the list of special actions, poses or idles. (or loading them and editing that in the Animaze Editor and doing in in the Animaze Editor UI).