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.