If the cut goes through the casing, you need to place a “boot” on the inside of the tire. Cloth sports tape or duct tape works well as a boot.

But this is just a temporary fix. Eventually, the tape will wear through, the tube will pop out of the opening, and it will puncture.

To protect the boot from wear, place some Shoe Goo on the outside of the tire. This stuff sticks well and is very sturdy. Wait at least a day before using the tire.