How can I get my son's father's rights terminated?

My 2 year old's father is consitently getting arrested, getting into fights, is drunk and disorderly. For the year we were together he lied about where he was and what he was doing. Now that I have had to pay to see his police records I am sickened knowing my son HAS to see him. Visits are supposed to be supervised but they aren't completely. In August he threatened to kill my fiancé in front of our son. This irratic, irrational behavior is not ok. He is extremely violent, suicidal, intimidating. On father's day he was supposed to have our son. Our son was picked up for his visit and his dad never came. I read in the police reports he was taken to the hospital at 8:30 pm bloody and highly intoxicated. In September he was seen an 2:30 am harassing, pushing and choking an elderly mentally disabled man. In June 2013 he shot himself. This is just a bit of what I've found. If he shot himself what else is he capable of.