A few things to consider:
1) The sulfur present in onions gives them the sharp/hot taste/smell. This will vary from variety to variety, as well as from field to field, as some growing areas don't have a lot of sulfur in the soil. This is why Vidalia's are so sweet, the variety doesn't fix much sulfur into the flesh, and there's not a lot of sulfur present in the dirt around Vidalia, Georgia (or where ever they come from).
2) Make sure your knife is really, really, sharp. If your knife is dull, then you aren't cutting the onion so much as you're bruising it, and releasing more of the juices.
3) I refrigerate my onions. Keeping them cold really helps in not letting the juices evaporate into the air as you're cutting them.
Peace, Love, and Vegetable Rights!
Eat Meat and Save the Plants!