I'm going to report my employee to state tax authorities
Why would you do that to an employee of yours?  Have they broken the law?
The way he works absolutely annoys me
It's wrong to try to get revenge on people just because they annoy you, but I'm assuming this employee of yours is also breaking the law? If so, it's responsible of you to report his criminal activity to the state. Lawbreakers should be punished.
He was even bragging about not having a big tax bill.
If he was bragging about criminal activity, then that is a legitimate reason to report him.  However, you should recognize that having a big tax bill doesn't mean that someone has broken the law.  He might just be bragging about how much money he earned on the side, which left him with a bill that he is fully prepared to pay.