While I was looking for resources on prehospital amputation, I came across the videos below from the Trauma surgeons of the Medical College of Wisconsin. They also have a webpage specifically for the procedure.
Here is their field manual that describes the procedure
Introduction and Background Video
Upper Extremity Video
Lower Extremity Video
Cliff Reid has a post on the procedure, that pointed to this article:
Porter KM. Prehospital amputation. Emerg Med J. 2010 Dec;27(12):940-2.
Sydney HEMS has a video of an amputation of a deer leg
I discovered this article thanks to the excellent Trauma Professional's Blog:
In-Field Extremity Amputation: Prevalence and Protocols in Emergency Medical Services. Prehospital and Disaster Medicine 11(1):63-66, 1996.