Shoe repair for small cuts or tears

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The cut is very clean. Barge cement and then sand off any excess so there is hopefully just a razor thin line of the slick adhesive?  Just want people’s thoughts before I do something dumb

I think you can just use some Freesole on it. No sanding necessary.

If the cut is from gradual use and not any specific incident, that means the rubber surrounding the area is also thin. These shoes are resolable; I'd suggest doing that before you see leather (or the next layer of rubber down), as, in that section, the rand and midsole are tightly/precisely layered and replacing the rand is not preferable (or cheap). Freesole will do ok..ish. Sticking barge cement in the crack with an awl and getting things tight is the best option for a quick and  dirty repair but it's still sub par, especially if you are climbing on that section of the toe. Resole is worth it on those shoes price wise! $48-$68 or do, depending where you go. 

Source: I resole shoes. 

Any gluing is going to temporary at best but hot glue is better than barge cement. Resole is best option. 

Not to hijack the thread, but what's the difference in freesole and barge cement? I have both but haven't used either too extensively.

Free sole is urethene and will set on it's own. Contact cement is a glue that's well loved because of the holding power and the fact that it remains quite flexible. Free sole is good if you need to create volume or a thickness, or abresion resistance. It can help to think of free sole as a material and contact cement as more of an adhesive.