Why is there green pus coming out your dogs tick wound?

Green pus indicates an infection. It's possible your puppy has Conjunctivitis, or another eye infection. Your puppy should be examined by a veterinarian, and probably requires medication to clear up the infection.

Conjunctivitis is easily treated, but it's important to diagnose and treat conjunctivitis in quickly, to avoid serious risks such as visual impairment. If left untreated, the infection that caused conjunctivitis slowly spreads to other parts of the eyes damaging the puppy's eyesight.