Normally I don't eat with a tie on. The community I live in tends to be fairly informal in matters of dress, so a tie is usually not needed, and certainly not for meals. If an occasion is formal enough to demand a tie, it's clearly too formal for my messy eating habbits!
However, if it ever does happen, I just slip off to the restroom and wash it out. Almost any food stain will wash out easily with cold water if you get it right away before it dries. This is also what I do whenever I spill something on my shirt, which happens with some degree of frequency. (Yeah, I eat with a shirt on all the time. We're not *that* informal in Galion. Sometimes even a button-down-the-front shirt with a collar, e.g., if I work a long shift at work and eat in the middle of it.) I wouldn't want to ruin a perfectly good tie, just because I spilled a little food. I paid as much as $5 for some of my ties.