Due to a malfunction the rig crew was instructed to lay down the Measurement While Drilling (MWD) tool. The make-up tong was placed around the mud motor and latched. The break-out tong was placed around the MWD tool and an attempt was made to latch the tong when the injured person (IP) placed in the thumb of his right hand between the lever and the long jaw of the tong. His thumb was caught between the jaw and tong body, removing the flesh from the end of his thumb. The removed flesh could not be reattached and the bone had to be amputated and the stump of the thumb sewn closed.