Joe is friends with both guys -- and says it's crazy to watch them bash each other so hard on social media.
The latest in the feud ... Floyd says 50 Cent is a "herpes infested rat." 50 says Floyd is a fake rich "sucker" who beats women.
50 also made some dark accusations about Mayweather's alleged role in the murder-suicide of one of his friends.
Enter Fat Joe ... who says he still believes in his heart of hearts that Floyd and 50 love each other -- but believes they need to call a truce.
"I'm tired of being the middle guy," Joe said ... "I'm tired of [being] the guy breaking everything up. I mean, you know, they're brothers, man. I don't like it. I don't like it. Because they're both beautiful guys to me, man."
Despite the hostility, Joe says there may be peace "somewhere down the road."
"I think maybe in the long run, they'll figure it out. I really believe that they sincerely love each other and they're brothers. Unfortunately, this is playing out on social media."
Meanwhile, Fat Joe is killin' it in the studio -- he just released a new track called "Attention" with Chris Brown.