Super Glue is no longer a good product due to bumbling morons gluing various body parts together, and a preservative was added to make the shelf life longer which in turn made the glue brittle. I used the stuff for years on tire cuts, even carried it in the saddle bag, but no more.
Gorilla Glue Super Glue is now a better option. Gorilla Glue Super Glue even added liquid rubber to the glue which gives it shear strength something like a cut on a tire would need. Even regular Gorilla Glue will work but it takes longer to dry thus not suitable for a side of the road repair, and it will foam and dry with a bubbly brown hard mess, but it can be scrapped off and whatever you can't get off will be worn off in about 5 miles. Gorilla glue SuperGlue will dry in about 30 seconds, great for on the side of the road repair.
There's another product called Zap Gel found at The Hobby Lobby and other hobby stores might also have it. I have NOT used this stuff yet on a tire, but I heard from a buddy who tried it on a tire and loved it. It's small enough to fit in a saddle bag but it's expensive at $8 or so for a 7oz tube.
Shoo Goo is also great, but the cure time is too long for on the side of the road repair.