Doomsday kills Superman in the comics through a relentless assault. His raw power and aggression overpower Superman, and there's no let-up. It's a tragic and intense battle that ends with Superman's demise.
Well, Doomsday has this insane strength and just goes all out on Superman. It's a non-stop onslaught of punches and attacks that Superman can't withstand. Eventually, it's just too much for him.