How about putting the student in a different class while they ‘investigate’?
If the teacher really did ‘cut his lip’, then maybe the teacher has some issues that need dealt with.
I wish all the teachers did when I was in school was throw pencils. I had several months when I was in 5th and 6th grade where I had trouble sitting thanks to “Mr. Clark”, and I thank him to this day.
My guess is that the investigation will conclude with the student learning a costly lesson in the consequences of filing false reports.