My experience has been with the anime and its OVA about him, so I'll explain his backstory with that.
A criminal thug in Tokyo prior to the earthquake that destroyed the city and infected a small number of people with branch of sin, he was one of those who developed abilities. His blood ability was the ability to form his blood into blades. Two years after the earthquake, he is a cop, using his branch of sin instead of police issue weapons, he has a pair of serrated rings to slice open his forearms. He is the informal protector of an orphanage run by a young woman, and when he saves one of the boys from two muggers, he attracts the attention of another, more experienced, Deadman (branch of sin user) with the ability to cast his blood like spider's webs, and choke or tear people apart. He asks Senji to join him as the second in command of his army of gun toting thugs in their quest to form a new world order, but Senji declines, due to his life as a cop. The next day, seeing smoke, he runs to the orphanage to find all the children and the woman who cared for them have been brutally murdered. Demanding an explanation from the other Deadman, he is told it was done to free him of his responsibility, and so now he is free to help them reshape the world.
Senji launches an attack on their group, and is reinforced by his friends from the police force, which is successful. A few years later, during the anime proper, he is seen in the Deadman Wonderland prison, G block with the other Deadmen and is the first one encountered by the protagonist, Ganta, who is able to shoot his blood like bullets. Senji now has a tattoo above his eye, the initials of the members of his old police squad, who it is implied he killed (possibly by accident) between the OVA and anime. It's probably this that got him put on death row. He expresses a lust for violence, and loves challenging combat, and is widely considered one of the most proficient Branch users in the facility, described as 'an old hand at Hemoglobin Homicide'. When offered the opportunity to lead an escape from the facility, he declines, stating that the world is run by survival of the fittest, and that at least in the Wonderland, it was straight forward.
He's Ganta's first opponent in the 'Carnival Corps', a match to incapacitation or death between Deadmen and is thrilled to fight, to the point where when a doctor tried to postpone it due to Senji having broken ribs and a cracked sternum from a previous altercation, he nearly killed her.
'As soon as that buzzer goes off... I'm gonna fuck you up, man. Little kid, or not!', Senji.