Bleeding and swelling are common physical responses to injury, and can be caused by a variety of factors including accidents, bites, and even overexertion. In cases where your dog's paw may be bleeding, it's essential to provide prompt first aid and carefully clean the wound to prevent infection. While it's true that a light cut may heal on its own with time, it's important to observe the area carefully and keep a close eye on your dog's behavior for any signs of discomfort or distress. In more serious cases where the cut is deep, it may be necessary to seek veterinary care and have the wound stitched up for proper healing and to minimize the risk of complications. Remember, it's always better to err on the side of caution when it comes to your pet's health and well-being.