There is a way to do that. It's in the Media Management tool, under the file menu. It has plenty of options. You can go clip-by-clip, do a whole timeline at once, or archive a whole project once you've finished editing it, and keep only the footage you used. You can also add "handles" if you want, which means that Resolve will save an extra second or so (user definable) to the beginning and end of all clips, so you have wiggle room in case you need to make changes later. There's also options for transcoding, if e.g., you wanted a smaller footprint for old projects, but it also comes in handy for generating proxy media.
A big word of caution, though: Not all of the features in the Media Management panel work like you might expect (the automatic re-linking comes to mind). Some of them are contingent on the TYPE of footage you're using; whether it's intra- or inter-frame. READ THE MANUAL, and BE SURE you test your Media Management workflow, COMPLETELY before you destroy any of your media. That is, don't just export it, and trash all of your originals before you make sure you can re-link your project. Ideally, you should:
- Use the Media Management tool to render out whatever clips/timelines/projects you want to trim.
- Take the original media (but not the archived media) offline. It can be tricky to do this if your projects aren't organized. An easy way to be sure is to keep your original media on an external hard drive, and eject the hard drive for this step. You want to be sure that when you delete the originals, your timelines can find all of the archive material they need, without accidentally pointing at things you're about to erase. If something in your project is living in your "Downloads" folder by mistake, it'll eventually go missing.
- Re-Link your project to the archived material, and make sure everything works. It may be years before you return to it, so you want to be sure it's in working order before you put it in cold storage.
- Export a .DRP project file and save it next to your archived media. Resolve's normal way of saving is database-driven (disk databases by default, now, but postgresql is necessary for advanced features). It saves all of your projects together in a big file that isn't meant to be moved around, and is vulnerable to corruption. If you're ever going to return to the project you're archiving, don't count on the database.