1. Two parties looking to beat each other up, or 'knock the snot out of them', whether it be 2 fighters, 2 sports teams, etc.
2. What a woman has once someone sneezes on her chest.
"The Skins and Eagles are both snotknockers tonight - they just came to crush eachother and see how many players they could take down!"
"Achoooo!" "Damn, did you have to sneeze on my tits?!" "Haha, now they're snotknockers!"