Preheat the oven to 400 degrees. Toss the carrots, parsnips, and beets with 2 tablespoons olive oil, salt, and pepper on a baking sheet. Roast for 25 minutes until the edges turn golden.
While the roots cook, season the venison with salt, pepper, and rosemary. Heat the remaining tablespoon of olive oil in a skillet over medium-high heat. Sear the tenderloin on all sides until browned, about 8 minutes total. Add the butter and garlic to the skillet and baste the meat for 2 minutes. Remove the venison and let it rest.
In the same skillet, add the blackberries, red wine, and balsamic vinegar. Simmer for 8 minutes, stirring and pressing the berries until the sauce thickens. Slice the venison and serve it over the roasted roots with the blackberry reduction spooned on top.