In a saucepan, combine water, chicken broth, olive oil, butter, garlic, and hot sauce; bring to a boil. Reduce heat, and stir in vinegar. Season with parsley, basil, rosemary, cumin, paprika, salt, and pepper. Simmer for 20 minutes, stirring regularly. Allow to cool.
Pour cooled sauce over venison steaks, and marinate in the refrigerator for 3 to 4 hours, turning regularly.
Preheat an outdoor grill for high heat and lightly oil grate. Take steaks out of marinade, reserve marinade.
Grill steaks for 7 to 8 minutes per side, or to desired doneness. Turn them regularly and make sure you don't over-cook. Mop steaks with reserved marinade while cooking.