The exFAT format is compatible with different computer operating systems but it's not Apple Disk Utility's liking. That's the possible reason causing the Disk Utility can't repair this hard drive on your Mac trouble. You can try to fix the trouble by repairing the hard drive in Single User Mode or a hard drive reformatting. Since you need to use it on multiple operating systems, the reformatting option is less recommended.
How to fix Disk Utility can't repair this disk on Mac by launching Single User Mode:
1. Restart your Mac and, before the Apple logo appears, hold down the Command + S keys to boot into Mac Single User Mode.
2. Type in:
/sbin/fsck -fy
3. If you see "File system was modified", then re-type in the command above again until you see "The volume _ appears to be OK".
4. To restart your Mac, type in:
reboot
If this method fails to repair your drive on Mac, you'd better repair your drive on a Windows device instead.
