Axel was originally a planned character for the game, but he was ultimately cut. While he's absent in the game itself, there is evidence of his development and scrapped content, including an early concept art image that can be found online.
If you're looking for a character with a similar style to Axel, you might enjoy playing as Sweet Tooth. He's a classic Twisted Metal character known for his aggressive gameplay and unique vehicle, the "Ice Cream Truck of Death."