Q: Why won't my external hard drive open

If Disk Utility recognises it, what does it say about the format (bottom left of DU window). It should be Mac OS Extended (Journaled). Try a Verify Disk, (button at bottom right) and repair if needed. Also in Disk Utility, do a Repair Permissions on your Macintosh HD.

You can also test the external drive connection with a different USB cable.

If nothing else works and you feel confident enough and have the tools, you could try switching the drives in your two enclosures to find out if the enclosure is at fault. Presumably the other HD is working all right.

Please read this whole message before doing anything.

This procedure is a diagnostic test. It’s unlikely to solve your problem. Don’t be disappointed when you find that nothing has changed after you complete it.

The purpose of the test is to determine whether the problem is caused by third-party software that loads automatically at startup or login, by a peripheral device, by a font conflict, or by corruption of the file system or of certain system caches.

Disconnect all wired peripherals except those needed for the test, and remove all aftermarket expansion cards, if applicable. Start up in safe mode and log in to the account with the problem. You must hold down the shift key twice: once when you turn on the computer, and again when you log in.

Note: If FileVault is enabled, or if a firmware password is set, or if the startup volume is a software RAID, you can’t do this. Ask for further instructions.

Safe mode is much slower to start up and run than normal, with limited graphics performance, and some things won’t work at all, including sound output and Wi-Fi on certain models. The next normal startup may also be somewhat slow.

The login screen appears even if you usually login automatically. You must know your login password in order to log in. If you’ve forgotten the password, you will need to reset it before you begin.

Test while in safe mode. Same problem?

After testing, restart as usual (not in safe mode) and verify that you still have the problem. Post the results of the test.

Hello.  I was hoping that you will be able to help me, as I have the same issue with my external hard drive.  My computer froze a few days ago while it was updating the Safari software. So, I had to restart it in Safe Mode and now when I try to open my external hard drive, it won't open. It's recognized by my Mac though. And my VCL and Quick Player also doesn't work anymore. Help please! Thanks in advance!

See mount section in 1st linked article.

Disk Unmount Using Terminal

Disk Utility – Force Mount Disk

Try running this program in your normal account , then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor.  Please use copy and paste as screen shots can be hard to read. On the screen with Options, please open Options and check the bottom 2 boxes before running. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.
  

Etrecheck – System Information