Oh -- I missed the "not delivered" indication, sorry.
Huh. It looks like you're sending via Messages. I played around with sending a photo with Messages from an external hard disk drive but didn't notice anything odd...
Your external drive is probably slower than your internal drive, but it shouldn't make any significant difference. I'm assuming you're not disconnecting or ejecting the external drive before the photo is completely sent (which can take awhile). I'm also assuming the photo on the external drive is just a file you're accessing with Finder. Or, is it in a Photos.app library, or some sort of archive (like a .zip file)? Does this problem seem to happen for any photo on the external drive, or just a particular photo?
Might be worthwhile to copy the photo(s) to a different external device (a HDD or a USB flash drive, for example) and see if you have the same behavior -- to determine whether the issue is specific to a particular device.
So far I'm at a loss to explain why you're seeing this issue! Very odd, and it must be frustrating.