I had the exact same problem. I thought it was because I turned the main turret on defense mode, so the turret killed him, but no matter what I did, it still told me to deal with Jotaro, even though he was clearly dead. In my game, he was half a body. I picked him up to try to put him into a bin to finish it, but it wouldn't allow me.
The only way I fixed it was to leave the area, then it completed... but then I had a series of glitches that went on for ages. I kept being told I received new items, constantly, although I wasn't picking anything up. When I hacked, it would show a transfer of 0 to 0, then later show the actual transfer to my credits.
It eventually went away, but was super annoying.
Try to incapacitate him instead of killing. If you want to kill him by moral's choice, sneak behind him or blind him by quickhack, grasp him and break his spine. (It works. I tested.)
I can confirm that the bug occurs and sometimes (i.e. in my case) there is no way to work around it. Check my video on YT with the Jotaro quest. You can see that I tried to complete mission using 3 methods. Of course the total number of attempts is much greater... like about 20.
As for me i got this bug because i found Jotaro first before i completed the step "Enter the club" (or something like that) so i think the game got confused cause i completed one step ahead. I saw him standing in his room looking out the window which you can see from the alley and i tag him cause i thought he was normal enemy. Luckily i always save before i do mission cause i do my mission steathly so i have to save a lot, the solution for me is restart the mission from beginning and dont find Jotaro first before you get into the club. Hope this works for you guys, good luck.