Is this a brand-new drive, just out-of-the-box?
Or... is it an older one?
As Hobe mentioned...
IF it's brand new, your "first step" should be an ERASE & REFORMAT to Mac format.
It's a platter-based hard drive, right?
In that case, erase it to "Mac OS extended, journaling enabled, GUID partition format".
Also known as HFS+.
HOWEVER... and this is a special case... if it's going to be used for a time machine backup, erase to APFS, GUID partition format. APFS is now required for tm backups, I believe (I don't use tm).
Hmmmm....
IF it's a drive that you've already been using for a while, I'm thinking that the "Master Boot Record" (as revealed by disk utility) could be a problem, because that's a "PC standard".
If disk utility won't repair it and get it mountable, you might try to scrounge up an old copy of "Drive Genius". Try running the repair/rebuild option on the drive.
If THAT doesn't work...
... maybe you ought to take it to a PC and see if there are any utilities there that can help.