Can I save my highlights?

With the recent overhaul of the Highlights system it is now possible to export highlights as video files. It is also possible to record your own highlights, in addition to the automatic ones. Highlights no longer expire as soon as the client is closed, although they do still eventually expire — they must be exported to be saved permanently.

To export a highlight to save it permanently, go to the Highlights section from the main menu and press the "record" button on the highlight you want to export. (Click elsewhere to review the highlight.) This will present a dialog that can be expanded for settings to control the quality of the export — it will be re-rendered in non-real-time, so you can select the highest settings even if your computer would never really be able to play with them.

The exported videos will be added to your Documents folder, under Overwatch/Videos/Overwatch/.

I had the same issue, but sadly in the beta it's still not available as a feature. Though I'd love to save how I ressed 3 teammates at once with Mercy, or how I smashed a certain pain in the ass opponent in the wall with Reinhardt. Or just simply a few multikills with Bastion.

As for screen recording, if you use win 10, it already has a screen recording function for games, should work with Overwatch too. On basic settings, the recording can be started/stopped with the windows key + alt + R shortcuts. (Or at least I hope these are the basic controls for it, my PC offered me these as basic)

What I did was I opened OBS and just recorded the Overwatch window while playing the Highlight!

Hope this helps!