This may or may not be common knowledge to people, but I think it’s quite a new addition. You can now save your streams on the mixer website, and from there they can be downloaded. Much like you can do with Twitch, but this is far easier to do because of the integration within the Xbox Guide.
To set this up, sign into your account on the site Here , and once you have, click your account icon in the top right and navigate to ‘Manage Channel’ - on the screen you see, it should be on the Broadcast page. At the bottom of the right hand column here there is an option called ‘Keep recordings (VoDs) of my streams’. This won’t be on by default, but if you turn it on and save the selection, it will now store your streams!
To access your streams to download them, on the screen you were just on select the tab titled VODS, and they will show up there. You can watch, download or delete them from this screen, and they seem to have an expiry time on them of two weeks after streaming.
Here is a video I made to test it out.