Spitz dies in a fight to the death with Buck in chapter 3, "The Dominant Primordial Beast," of The Call of the Wild by Jack London. This is a crucial step in Buck's transition from a domesticated house pet to a dominant leader well able to survive amidst the savage Northlands.

Due to the need for sled dogs in the Klondike gold rush, Buck is stolen from his pampered position in a judge's home in the Santa Clara Valley, crated, beaten, and eventually sold to two French-Canadians in government employ who train him as a sled dog. Chapter 3 of The Call of the Wild tells of Buck's rivalry with Spitz, the leader of the pack. At first Spitz has the upper hand due to his fighting experience. However, what Buck has going for him is his intelligence.

He was preeminently cunning, and could bide his time with a patience that was nothing less than primitive. It was inevitable that the clash for leadership should come. Buck wanted it. He wanted it because it was his nature, because he had been gripped tight by that nameless, incomprehensible pride of the trail and trace...

The showdown between Buck and Spitz finally takes place during a chase for a rabbit that turns into a fight to the death. Spitz initially has the upper hand, but then eventually Buck breaks both his forelegs in his powerful jaws, and the rest of the pack rushes in to finish Spitz off. The rivalry between Buck and Spitz as well as the final showdown all take place in chapter 3.

The dog Spitz dies at the very end of Chapter 3.  That is the chapter that is entitled "The Dominant Primordial Beast."

Spitz dies after a long chase and a fight with Buck.  The two of them have been contending for power within the pack all through this chapter.  Buck has been undermining Spitz's authority for a long time and he has finally taken the opportunity to pick a fight to the death with Spitz.  They fight for a long time, and Buck finally gets Spitz down.  At that point, Spitz dies just the way he killed Curly earlier in the book.