As Deadpool states, Ajax is a dangerous, murderous psychopath, without any hope of redemption. Why would Colossus want to keep him alive (and somehow links Deadpool "being a hero" with not killing him)?
The movie hints strongly at a backstory between Deadpool and the X-Men, which unfortunately we don't get to see any of that. However, based on Colossus's preaching at him, I think we're supposed to recognize that he's been chastising Deadpool for his excessive violence for a while. Deadpool, for his part, acts as if the X-Men are constantly trying to recruit him to their cause and he's constantly turning them down.
As such, I think that the Ajax situation isn't so much about Ajax as a person, but rather, Colossus is trying to change Deadpool's overall behavior of just killing everyone that gets in his way. He's trying to show Deadpool that there's other alternatives besides mass murder, and hoping that talking him out of murdering Ajax would be a good start.
Also, note that in this movie, probably even moreso than in a typical (non-Snyder-non-Nolan) superhero movie, Colossus is playing the totall straight, by-the-book good guy, who never hurts anyone he doesn't have to, helps the enemies out when they're injured (e.g. see how he treats Angel later on), etc. So no matter how bad a person Ajax is, Colossus's characterization in Deadpool requires him to want "legal justice" -- arrest, detain, try, etc.