If you cut yourself when do you need stitches? When will skin glue work? Of course not all wounds need to be closed.
If the skin is torn off, there probably won’t be anything to grab on to to suture it together. Unless the wound is large, you can wash it out carefully with soap and water frequently. You should watch out for signs of infection such as redness, pain, discharge and fever, If these occur you will need to be examined by a doctor as soon as possible. If you think there might be a broken bone or some foreign body within the wound you probably should go to your doctor as well.
Cuts that are larger, over joints and within your mouth will most likely need to be sutured. This is because skin glue will not hold against joints that are moving and in the case of cuts within your mouth won’t work well.
Remember that both stitches and skin glue can increase your risk of infection. Your doctor might consider prescribing antibiotics in such cases. Also if the wound is heavily contaminated, if it has been several hours since you cut yourself or if you have serious illnesses such as diabetes or cancer, your doctor is more likely to give you a prescription for antibiotics.
To suture a wound, the wound must first be prepped or the skin around it cleansed of bacteria. The wound is then numbed up with local anesthetic, irrigated with water or irrigating solution and then sutured. Sutures will remain in the wound anywhere from 5 days to 2 weeks or more, depending on the location. The sutures are easily removed by your doctor.
Bottom line is that not all wounds are equal. If you have concerns see your doctor.