When Maximus is knocked to the ground he lands a shot through his opponent's foot with an axe. His opponent then seems to be spitting blood (hard to tell due to the helmet) and then falls over dead.
Why did he die?
This is from the script. I couldn't find a video. The blood probably comes from the blow to the head. Tigris was pretty injured from this hit but was probably trying to hold back any sign of his being hurt that bad until the axe went into his foot and he couldn't stand the pain so the blood that was in his mouth from the hit to the head came out at that time.
Maximus finally manages to land a stunning blow to his opponent’s head causing Tigris to drop his axe. Maximus switches his sword to his other hand and stands ready to administer the killing blow. Suddenly a fourth tiger jumps out of the last door and leaps on Maximus and just as quickly, Maximus twists and turns his sword arm, impaling the tiger. He is thrown to the ground by the weight of the beast all the while stabbing and eventually killing the big cat. The crowd cheers.
Tigris seeing an advantage moves closer. Maximus, pinned under the weight of the tiger, reaches out and grabs Tigris lost axe. The axe has a spike on one end and in one movement; Maximus brings the spike down and into the top of Tigris foot. Tigris bends over from the pain, blood pouring from the mouth of his mask. Maximus jumps to his feet and kicks Tigris to the ground. Maximus standing over the fallen Tigris lifts the other man’s face cover and raised the axe. He looks to Commodus for direction. The crowd yells.