There was the option to cut off the immortal power's serpentine mouth. But he went for the neck. He didn't just stop after shutting off the cry. He tried to remove the power immortal's head completely from his shoulder. The immortal power died because of Soverick's overzealousness in shutting him up.
"What a crybaby," Soverick muttered. "I'm sure it wasn't that bad."
He is speaking from experience. The consequence of his fight with the dragon in the first challenge is the most painful thing he has ever experienced. But he still had the mind to sneak into the law matrix and decode it secretly while he healed. So he knows what it feels like to have the framework of your existence crushed. Then again, he and other clones of Legion have been unnaturally comfortable with pain.