Ok soooo I was raised in the south and the "breaking a foot off in his ass" discipline thing isn't real here. There are multiple red flags going on here between how you discipline your child and your relationship.

1) 6 months is wayyyyyy to early to considering marriage. Especially with children. Tbh 6 months is a good time to be slowly introducing your bf to your kids. Don't rush into anything when you barely know the guy. You are already having problems because of difference in parenting between you two. And of course because of your son. You need to take things slower.

2) you need to discipline your child. I'm not approving what your bf is saying, but he's saying these things out of frustration because your child has no respect. And he doesn't do anything because he barely knows the child and probably doesn't feel right disciplining him. When he wont pick up his toys, take them away. If he back talks tell him he's not allowed to speak to adults with such disrespect and there will be punishment. No TV time, sent to bed earlier, anything. Disrespect isn't something kids just "grow out of". You not doing anything just lets him think he'll be able to get away with talking to you guys like that.

3) the way this guy is talking about your child. You guys have only known each other 6 months and he's already showing signs of aggression. You shouldn't let a guy who wants to slap your child even be around your child. Your mommy-defense radar should be going off the walls.

I think the best solution is to split. You have different views in parenting and discipline. Huge factors for marriage. And as long as your son is acting up, your bf isn't going to get any better. He'll just become more angered. If 6 months you're already having bigger issues, it's usually not a good sign.