You know 事 means "occurrence," but it can also mean "matter." And someone who handles punishment matters is someone like a police detective (or detective) trying to find and punish the bad guys.

刑事 isn't an official job title but a common way to refer to a police officer whose job is to investigate crimes and arrest criminals. Depending on the context, it can also refer to matters that fall under criminal law, like 刑事事件 (criminal case).

This is a jukugo word that uses the on'yomi readings of the kanji. You should be able to read this on your own.