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.

Field Manual

Here is their field manual that describes the procedure

Introduction and Background Video

Upper Extremity Video

Lower Extremity Video

Review Article

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.

Gigli Saw

Sydney HEMS has a video of an amputation of a deer leg

References

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.