Hi, Danah,
Thanks for visiting the Apple Support Communities. I understand from your post that you are trying to trim videos in QuickTime player, but receive an error "This operation could not be completed". I'm happy to help!
The first recommendation I can make given your situation is to quit QuickTime: Quit apps on Mac - Apple Support, and then restart your Mac: How to turn your Mac on or off - Apple Support.
If the issue continues after that, see if it persists in a new, test user: How to test an issue in another user account on your Mac - Apple Support. And if so, does the same issue occur in another app, like iMovie: iMovie for Mac: Trim clips?
Should you still need help, don't hesitate to respond back. If you do, please include the answers to the following questions:
- Where were these movies downloaded from?
- Have you ever been able to trim/edit movies in QuickTime from this source?
- What is your current macOS version (example: macOS Catalina, Version 10.15.2)? You can get this under the Apple menu > About This Mac.
Have a lovely day!