In God of War IIEdit
After weakening them, Kratos can kill the Griffins by leaping off Pegasus and onto their back, slicing both their wings off simultaneously with his blades, and then impaling the now wingless creature in the back, and throwing it down to Earth.
If a rider is on the Griffin, Kratos will first fight the rider and knock them off to kill him, and then rip the Griffin's wings off with his blades or his bare hands.
Griffins are only seen during Kratos' journey to the Island, when Kratos rides the Pegasus. The Dark Rider, rider of the Dark Griffin is presumed the leader of the Griffins and the riders who command them.