Give Users the ability to private clips they've made in the Clips Manager. Select the clips you want to make private and they would gain a lock symbol next to them and they would not show up on the clips page. Locked clips would be Prevented from being shared and if you would like to make them public again they would need to be approved by the Channel Creator or mods. The Channel Creator Could see a list off all the Private Clips and be able to delete them if they feel the need to.

Sometimes there are situations where you might want to hide a clip for one reason or another for a specific amount of time (For example: Let's just say that one of your clips is getting not wanted attention, but you don't want to delete the clip, you just wanna hide it for a specific amount of time). So it would be great if Twitch had a visibility option for clips. This can be done by two ways:

Either the VOD/highlight way of: Publish/Unpublish

Or have a YouTube like feature which allows to switch clip between:
Public - allowing everyone to see it,
Unlisted - Allowing people with a link/editors to see it, and
Private - self explanatory.

Do not know if this has already been suggested, since there is not a search function for this, but having the ability to hide/private your clips, vods, and highlights both created by you and your viewers, especially for DMCA material. This would then allow streamers to review their material at their own pace without worrying about publicly viewed clips or vods. They could then decided to delete, export, or re-release their vods and clips to the public.

Haven't checked recently but I do not believe there is a mass export of clips either. This seems like an essential feature to quickly review your clips.

Unlist vods and clips

I would like being able to ecord a clip from a streaming and save it in a way that only me or the people I choose can see it.

Now I can use "public" when I upload video. This is very good service. But I want "unlisted".