You use a dremel cutting wheel. If you never used that before be careful and always wear eye protection.
You want to "saw" back and forth and work your way through the hook eye. If you just put the wheel down on the hook and do not "saw" you make a groove the same shape as the wheel and the friction force will make the wheel jump forward - often resulting in a slight twist of the wheel in the groove causing it to break. If you "saw" then you have only one point on the wheel touching the steel and the friction force is low. Also be sure not to twist all all once the cut gets a little deep. The wheel will bind on the sides of the groove and you will get that jump/break thing happening.