What sort of tire and how thick is the tread? 1mm is nothing in the centre of the tread of a 28c commuting/touring/winter tire, but a whole lot near the edge of the tread on a 23c racing tire.
If you're sure the casing is good, I would pump it up to max rated pressure and go for a ride in a controlled environment (e.g. bike path) and see if it splits open any further; do a few sharp turns to stress it*. If it doesn't split open any further, I would continue to ride it**, as a rear tire only.
I very much doubt you could repair it in any way; the stresses involved are much higher than rubber cement will cope with in such a small surface area. I used to repair my own climbing shoes, and even though one could throughly clean the surfaces and prepare them for the cement (grinding the old rubber away works best), then heat the surfaces while pressing them together, and cure the bond under compression, the glue is not as strong as the rubber. It works fine for climbing shoes because the forces involved tend to push the joint together, but cornering (and inflation) forces on a tire tread will both tend to spread a longitudinal slit apart.
Little harm in trying to repair I guess other than wasted time and cheap tube of cement...general rules of rubber bonding are: clean thoroughly (e.g with acetone/isopropyl alcohol), apply minimum adhesive to both surfaces, keep surfaces apart until adhesive touch dry, heat surface (achieve heating and drying simultaneously with hairdryer is OK) and bring together, keep compressed until fully cured (12 hours or more) - turning the tire inside out might help compress the cut (assuming of course it's a clincher and you can actually turn it inside out).
Clear silicone adhesive. I use one called Permatex to fill holes in my tires and it works great, I'm sure it could fill a small shallow slice like yours pretty well. You can get small tubes of it for micro applications at any good hardware store.
i addition to the above, you can 'boot' the tire from underneath. to do that
you cut a piece of old tube and put it under the cut. it does work, although
only for training/commuting i would say. out on the road i have used pieces
of plastic when necessary. an old school patch for sure.