If you have a deep cut and is bleeding, the first thing that should be done is to stop the bleeding. A clean towel would usually be fine if it is not bleeding profusely, Apply pressure on the wound. Try to hold the skin together. If blood leaks out from the towel, layer another towel on it. Do not remove the first towel as it takes off the blood clotting substances that stick to the towel. (The blood clotting substances will stop the bleeding.)
If able to, clean your wound with water or alcohol swabs before applying an antiseptic. If it is an open wound and it really hurts to touch it, you may move on to using a bandage until it dries up, then apply antiseptic to prevent infection.
If your wound is not dry, DO NOT use a gauze. The gauze fibres will stick to your wound and will cause difficulty(even pain as you try to pull it off, because it pulls open your wound too!) to remove the gauze. However, if you do experience sticking of the gauze and difficulty(and pain!), you may dip your finger in water and wet the gauze slightly. This will slightly loosen up the gauze from the dried blood. It is more advisable for you to use the triangular bandage, fold in neatly to cover the wound and secure with a bandage.
Seek a physician's help should you find pus(yellowish substance) forming in your wound. This is a sign of infection.
Deep cuts leave hardly removable scars. But attempts can be made to lighten and smoothen your scar. Vitamin C to support healing and prevent infection, Vitamin E to keep the scar moist, and scar healing remedies like Rose Hip Oil or Mederma Scar Cream. I have a deep cut on my forearm and I use these to aid my scar healing. It's a little slow at lightening, but the scar is definitely less raised right now.
ALL MATERIALS USED SHOULD BE STERILE!