I try to eat as much as I can before I can't eat it anymore. I know it is offensive but I'm not gonna sit there forcing myself to eat every last bite.
In China, they serve their food on plates that everybody shares. So it isn't like you have your own separate plate that you have to finish. Instead, everyone shares the same dishes but eating from them using chopsticks. So whatever foods I don't like or can't eat (i.e. I don't eat pork), I just eat from the other dishes.
It's a tough situation to be in when not eating something would come off as rude or inconsiderate, but you just have to own up to the fact that you can't eat anymore.