Is it safe to put superglue on cuts?

No, too risky: Although you may have heard of this being done, it is not safe to do so for all of these need to be considered: 1) depth of the cut, 2) location of the cut, 3) possible tendon or ligament involvement, 4) possibility of infection, 5) possibility of wound dehiscence/re-opening, 6) sterility of the super glue, 7) length of time from the cut to time of repair, and 8) proper alignment of wound edges.

NO: Conventional superglue acc has toxic chemicals in it. Emergency and surgical centers have a product called dermabond which is safe.