tyres that are badly worn need to be replaced. If a new tyre gets cut it may be repaired.
Small bike tyre Cuts
Fold the bike tyre to open the cut.
Clean the sides of the cut with a fine file, emery board or sandpaper.
Apply a drop of super-glue to the clean sides then fold the bike tyre the other way to force the edges together.
Sand any excess glue from the outside of the bike tyre.
Larger bike tyre Cuts
Follow the steps above then reinforce the repair with stitches using dental floss