The following is based on Van Buren and has not been confirmed by canon sources.
Half-brother to Frieda Van Graff, Cutting was hauled off to prison a few years prior to the Prisoner's escape. Separated from his brothers and sisters he was unable to regroup with them by 2253. That is, if he is free, as it is not revealed.
In Fallout: New Vegas, Cutting has taken on the role of an enforcer, becoming the backbone of the Van Graff family security forces. He works in the Silver Rush alongside his half-sister, Gloria, and does his part in the politics of their operations in the only way he knows how; with the barrel of his laser rifle. He has Cutting as a surname, opposed to Van Graff, because it reminded his mother of her dead husband, who was also Jean-Baptiste's biological father.
Birds of a Feather, Heartache by the Number: Jean-Baptiste wants to have a little chat with a woman called "Cassidy." The Courier will need to find her, and bring her back to the Silver Rush. This quest requires committing to either the Van Graffs or Cass as it is not possible to satisfy both parties.
Jean-Baptiste Cutting has high health, more than most companions, as well as an incredible, and normally impossible, 117 Energy Weapons skill. The only reason for this seems to be to make him a "boss" character.
While armed with a laser rifle, he will usually pick up the plasma caster in the middle of the store if engaged in combat, unless it was previously stolen by the Courier.
During Birds of a Feather, when he confronts Cass and shoots her, he might shoot the floor or ceiling and Cass will still die. This is likely due to the fact that he is one of the only NPCs in the game that is fixed to kill another NPC by his own actions (i.e. through a quest).