While pulling out the tubing hanger, the driller and crew installed the landing joint and unbolted the Tie-down Bolts. Floor crew tried to install the Full Open Safety Valve (FOSV) to retrieve the tubing hanger, unfortunately while they picked up the FOSV from rig floor with the webbing sling, the FOSV was not aligned properly on top on the landing joint. It slipped from the double wrapped webbing sling due to its oily condition and it pinched the left middle finger of the Roustabout resulting in partial amputation of fingertip.