Superglue can be used to stop yourself or someone from bleeding.
I have used superglue when I had a cut that would not stop bleeding and although the superglue did sting a bit it did seal the cut and stop the bleeding.
So just be aware that the superglue may cause some stinging of the cut but the stinging should go away.
If you do have a really deep cut then you need to get to the emergency room to get stitches.
But if you have to use some superglue to stop a small cut then you certainly can.
Small cuts can also be stopped from bleeding by using Elmer's School Glue.
In fact I actually cut myself on the top of my hand today and put some Elmer's School Glue I had on available on the cut and it sealed within a few seconds and now the glue just wipes away and the cut is starting to heal.
The Elmer's Glue will peel off more easily from the skin and it's better than superglue for cuts.