Is it okay to put hand sanitizer in a deep cut?

Not recommended: Hand sanitizer has alcohol which can be toxic the tissues and flesh underneath the skin. (its not toxic to the top layer of skin) usually best course of action for a deep cut is to stop the bleeding with direct pressure. Then if bleeding stops wash with gentle soap and water. See a doctor to see if you need stitches.

Not optimal: Hand sanitizers often contain high concentrations of alcohol (like ethanol or isopropanol) which could be painful and injurious to tissue.