In order to save the leader from fraying in our fly school we tie a batch of yarn (or EP material) on the leader or tippet. Basically just cut a clump about an inch long on to the end of the leader/ tippet using a slip knot. This serves to both protect the end of the line and make the end more visible.
However, is the cut in your fly line? I have had that problem before (thanks dad). It was caused by me pulling a windknot in the fly line (not the leader) too tightly. The knot was clinched so tightly that the line was cut in half. In that case you want to cut the fly line off above the cut watching for any water in the line. If water seeped in then you want to find the extent of it and cut it there. After that then you can create another loop in your fly line for a loop to loop connection in the thread that somebody mentioned before. No need to spend money on new line... and thats coming from a fly line salesman