You can delete a Clip on the Timeline by clicking the small trash can next to the name of your Clip, in the same way you delete objects:

When you delete a Clip, you also delete all objects that are part of it. 

You can also delete a saved Clip from your Personal Library. To do so, select the thumbnail of the Clip in your Personal Library and look for the Trash can right above its preview on the right hand side: 

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