I'm going to ignore my dad all day after he made an offensive joke
Was that joke so offensive to you?
Yes, he's always making jokes about someone elses expense
I know you're upset but you shouldn't just ignore your dad. You should tell him what he said upset you.
Nah, I'm going to give him the silent treatment all day.
If you don't let him know that his jokes offend other people he'll continue to do so. Giving him a silent treatment won't change a thing. You should ask him to stop making such jokes.