Place the cutting board next to a gas range and turn on a burner or two.
The heat and flames draw in the onion mist, burn it, and send it up with the rest of the flame exhaust. In the heat the chemical changes such that it no longer irritates the eyes. One could also use the hood exhaust fan while the burners are on. The only drawback with this solution is that some unlucky fools aren't cooking with gas. They could try an electric range on high, but it doesn't really work (better to use several candles instead.) A poor stove arrangement might make it difficult or force you to cut left handed, but it can usually be worked out (and you don't have to stand very close to the flame). As with the fan, you want the flame to pull the onion fumes away from your face. And as pertains to all methods, you want to keep your face as far away from the hacking and hewing action at the cutting board as you can. I have a range with four burners: two on the left and two on the right with a big space between them where I put the cutting board. I turn on the two right burners, stand a bit to the left, and cut with my right hand.