If your drive is showing in the Disk Utility but not on the Finder / Desktop then most probably the drive is unmounted. Yes, it might be damaged or corrupt logically. You can perform below action.
Using Disk Utility, try to create a disk image of the drive. If successfully done you will have your files in the compressed format.
Now most important part; what’s the future of your drive? Look, if the corruption is logical then you can backup or recover files using any of the above 2 methods. Further, erase this drive with MacOS Journaled and it may come back to life. However, if the damages are catastrophic or physical then you might need to replace the storage media.
Run First Aid in Disk Utility to see if it can repair any minor errors on your external hard drive.
Use Terminal to detect, recognize, mount, and show your My Passport hard drive. (Follow the steps in this post and copy the command line if you’re not sure how to do it: Fix External Hard Drives Not Showing Up on Mac).
Reformat the hard drive if necessary (but be sure to recover your data first, as reformatting will erase all the data on it!).
Reset the NVRAM to help your external hard drive show up on the Mac.
Boot your Mac in Safe Mode and uninstall any third-party programs that might be preventing your external hard drive from mounting.
Open Disk Utility and look at the left panel. If the drive is there but looks greyed out, it probably means it’s not mounted. Try selecting it and hitting the “Mount” button at the top.
Still in Disk Utility, select your drive and run First Aid. If that also fails, it further confirms something’s off with the drive’s file system or hardware.
If you’re comfortable with Terminal, open it and type: diskutil list diskutil list
Then look for your external drive in the list and type: diskutil mountDisk /dev/disk2