How do I completely eliminate a file in Sierra? Not just encrypt it, but completely erase or eliminate it?

A third party secure erase app is necessary in Sierra and later.

File Shredder | Files, as Duchy777 mentioned, is one that gets good reviews. Note the specific name with the pipe. File Shredder is free, and only erases the whole drive. The same thing you can do with Disk Utility. That's actually all File Shredder does. It calls the Terminal command Disk Utility uses. File Shredder | Files allows you to erase specific files and folders. Cost is $5 and is available in the App Store.

I know you've said you're using a hard drive, but just as future reference, never try to secure erase anything on an SSD.

If you really want to secure the data, do what the government does for critical data. Take the drive out of the computer and whack the drive into pieces with a hatchet, or drill lots of holes through it with a drill press.

Unfortunately, any app that purports to "clean" a Mac is usually not recommended as they quite often will mess up your system by "cleaning" so well that they eliminate needed system files. I would strongly recommend to avoid any/all such apps. They should never be recommended here.

In reality, the only way to completely get rid of a file is to take out the hard drive/SSD and smash it with a hammer. If it is an SSD, the next best thing is to fill up the hard drive with large non-personal video files, boot into internet recovery, erase via Disk Utility, download/reinstall the OS. Then do the same thing again - twice more. At that point, only a specially trained person working at a government agency would be able to decipher your file.

Secure erase may still be available by the Terminal srm command. Try:

srm --help

Hi Hillary

You could try getting an app like Dr. Cleaner Pro and using the "File Shredder" sub-app which does a secure erase.

Good luck.