Our skin is a protective layer. The cause of cut injuries can be many, but first aid is not to repair a serious cut injury.
Minor cuts however can be treated as a wound.
First aid for bleeding is to apply pressure to the wound. A bleeding wound should always be kept as clean as possible, but the most important thing is that you stop major bleedings. Do not remove foreign objects in wounds, leave them there until help arrives.
If a person bleeds a lot, it may be to stop the bleeding. You may need to apply a lot of pressure to the wound to stop the bleeding. Press straight on the wound and cover with tight bandages.
If you don’t have bandage, use it you have to hand like cloth or curtains. The body tolerates a tight bandage for a while.
Large bleeding from arms or legs may be easiest dealt with by keeping pressure on the bleeding until help arrives. Only hospitals can repair cuts, but you can limit the damage by stopping bleeding and covering wounds.