Some situations work. "No offense but I need to end our phone conversation now". In this case you're clearing up something that would seem offensive on the surface but in fact is not offensive if you look deeply enough; maybe you have a doctor's appointment, and you don't want the person to get the impression that you hate talking to them.

"No offense, but I think you're mistaken"; some people take offense at being wrong about things, but sometimes people are wrong by no fault of their own and it can pay to point it out as gently as possible.

But you can't just say "no offense" and then follow up with anything you want and expect it to be OK. "No offense, but you're a filthy hobo and you smell funny and I hope you die, you ugly pig-dog" just doesn't work. I have heard "no offense" used in this way many times.