In the event that your finger is amputated during an accident, the American Academy of Orthopaedic Surgeons offers this advice:

• Apply pressure to the injured area immediately.
• Gently cleanse the amputated part with water (preferably saline).
• Cover it in gauze wrap.
• Put it in a watertight bag.
• Place the bag on ice.
• Do not put the amputated part directly on ice. You could further damage it.
• Take the amputated part with you to the emergency room immediately.

Source: www.sixwise.com