You can't save a gif by right clicking it on Twitter. But you can save it. Thanks to a number of websites like Tweet2Gif you can save it for download or make it a video.
1. Go to the tweet with the Gif
2. Click the more icon in the top right corner of the tweet.
3. Use Copy Link to Tweet
4. Go to the website Tweet2Gif or Google Gif from Twitter download, either on your phone or computer.
5. Paste the link and make either a Gif or an mp4 or both.
6. Then if you want to alter it (don't alter copyrighted gifs), take the mp4 into a video editing program and speed it up or down, etc.