My dad was a public school teacher and his last year got a class of “sweat hogs.” Three students were extremely disruptive, regularly. He went to the principal and said he wanted all three out of his class or he’d quit. Next day two were suspended but the third wasn’t. He told the office he’s stay until noon to find a sub. Later that week, the third student was arrested for stealing an 18 wheeler and driving it across the state.

There's also detention and "in-school suspension" (which is basically a big detention).

I think these punishments are commonly decided by administrators, not teachers. The teacher just reports them up the chain for misbehavior.

Suspension and expulsion are becoming embroiled in the anti-racism crusade due to some high-profile incidents, so blunt laws are being written to outlaw them altogether.