Is it normal to break and cut things when you get angry?

Whenever I get mad I break and cut things...I punch walls, people, or whatever is nearby. I've broken my knuckles a few times punching walls. I also cut things. Either myself or stab at objects near me. I have cut people before but not deep...more like scratch them with a knife. I have once or twice went to the pet store and bought mice to kill since they are cheap. At times when I don't act on my impulses I imagine myself ripping people's throats with my hands or teeth. Also at times when I hear stories or news of people suffering or dying I get very elated inside but never show it on my face and laugh when I am alone. Is this normal?