When running the first joint of 9 5/8 Casing, it was decided to check the float to ensure proper operation. The slips were set and the casing filled with mud. While in the process of picking up the joint casing and as the elevators were moving up to make contact with the casing collar, floorman prepared to pull slips with his right hand. Inadvertently he had placed his left hand on top of the elevator. His fingers were caught between the casing collar and the elevator. His left index finger was severed at the top knuckle and the middle finger tip was crushed.