I'm sort of spoiled here lately in that I have a quality, inexpensive processor 1.5 miles from my house. I take most of my kills to him. There are times where if I am giving the meat to someone else, but don't want to give them the 65.00 processing fee on top of it I'll butcher it myself. Other folks who I give meat to each year want it processed and we agree up front that they'll pay for that. In those cases they go to my guy down the road here too.
If I'm doing the butchering though, I cut the loins and backstraps out. Neck if it's large enough to bother with. Shoulders if they aren't destroyed by bullet or buckshot. When it comes to the hams I have a technique to debone them off the hanging carcass. Just cut around the "knees" (Do deer have knees?) and then cut around just above the hip joint. Connect those two cuts and then peel the meat from around the bone. Comes off in a nice big roast that you can then cut into steaks/stew/jerky/etc.
When I do this, I take a large cooler and fill it 1/2-2/3 with ice. I lay wax paper down across the ice and lay the meat on top of it. This keeps the meat up out of the water. I tilt the cooler on a block of wood and open the drain so the water runs out. Keep a check on the ice, replace as needed over 2-3 days (depending on ambient air temp) and then finish butchering and package.
As far as care in the field goes......gut quickly and get it cooling. No need to slit throats or anything. Do you really think it's gonna bleed more from the jugular when you've just opened it from stem to stern?? We use those cloth game bags to cover the carcass and hang them in a tree at our hunting location. If the weather is on the warm side (bow season) we gut, bag and run to the processor. It's about 30 mins from field to our processor. In cooler weather during black powder and gun seasons we'll continue to hunt and let one hang all day in a cool shady spot on the farm and then bring it in that evening.
NC Hunter's Education Instructor
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