I’m a student of the normal school.
I have just graduated from a formal school.
I have to do my normal but not formal exercises.
If I’m a formal student,and you steal my normal heart,then I’ll be a normal mammal in the formal stage.
It doesn't sound like a tongue twister to me. A tongue twister is something that causes a little difficulty when you try to say it. This seems pretty easy to say; even when I say it as fast as possible.
However, it does sound a little poetic and has a nice rhythmic feel to it. All except for the very last word. It seems a little out of place because it doesn't rhyme with any of the other words. If he changed that last word, perhaps he could put some music to it..