Thanks for reaching out the Apple Support Communities! That is a great question you have about syncing your Voice Memos to your computer to be able to delete them and I am happy to help! Please take a look at this link for information about how to Share and sync recordings from the iPhone User guide. This will give you the information you need to keep in mind when syncing memos to a computer along with the steps to take in iTunes to sync.
Next, if you are wanting to export the memos to an external drive, check out this article to Manage and back up your iTunes media library. Specifically, check out the steps in this section:
After you consolidate your media files, you can back up your library and media files to an external drive.
- Quit iTunes.
- Find your iTunes folder.
- Drag the iTunes folder from its location to an external drive. Your library and media files copy to the drive.
When you are in the iTunes Media folder, you will need to go to the Voice Memos folder and manually move the memos over to the external drive.
Next, to delete the memos from your iPhone, open the Voice Memos app and in the top left, you should see the option to Edit. This will allow you to delete the memos. You can also select the memo itself and swipe to the left to delete.