Cut the venison trim and pork butt into 1-inch cubes and place in a large bowl.
Combine the salt, black pepper, cayenne pepper, dried thyme, and Instacure in a small bowl, mix well, then sprinkle evenly over the meat.
Add the minced garlic and toss everything together until well coated.
Place in the freezer for about 30 minutes to firm up the meat to make it easier to grind.
Meanwhile, prepare the hog casings. Snip off about 4 feet of casing and rinse it under cool running water to remove any salt. Soak the casing in 2 cups of cool water and 2 Tablespoons of white vinegar for 30 minutes. The vinegar softens the casing and makes it more transparent. Rinse and drain before use.
Grind the meat. You can use a food processor and grind the meat in two separate batches, or use an electric grinder with a coarse #8 plate.
Transfer the meat back into the same large mixing bowl and add ½ cup of ice-cold water and mix thoroughly by hand.
Stuff the casing. Slide the casing onto a sausage funnel and stuff evenly, ensuring the casing doesn't burst. Tie off the ends.
Allow flavors to meld for at least six hours or overnight in the refrigerator.
Hang the sausage to dry at room temperature for about 1 hour.
Smoke the sausage at 180 degrees F to 200 degrees F for about 2 hours until it reaches an internal temperature of 160 degrees F.
Let rest overnight in the refrigerator before cutting into 12-inch chubs. Store in the refrigerator for up to 5 days, or vacuum seal and freeze for up to 2 years.