Take the stabby motherfucker, and then get another inmate who has a history of, and likes doing similar things...
Put them in a caged ring. Inside the ring are contact weapons of various types. Plastic riot shields, batons, maces, framing hammers, small shanks or fighting knives. Basic body armor also available to those who want to wear them. Kneepads, open helmets, elbow pads, light vest, that's it. Rules are simple: Whoever lives get to come out of the cage and serve the rest of his sentence. Match does not end until one combatant is killed.
And broadcast it on a special channel, in certain bars and lounges where people pay to watch, lay cash wagers, and bet on outcomes. Names/pictures/biographies of the combatants are published in a special pamphlet 3 days to one week before a scheduled match so bettors can lay wagers and finalize them beforehand. Different classes of wagers available too. Types of weapons likely to be used by each combatant, what type of armor they will put on before engaging, combatant martial background, fight/assault history, etc.
Recruits for the cage can be on a pure volunteer basis for inmates too. You want to serve your time in peace, then behave yourself. You want to fight, injure or kill someone, then sign up for the Cage. Assaulting a correctional officer or other staff, including medical staff, means mandatory cage match. Assaulting or killing another inmate for reasons other than self defense? To the cage. Get the picture?