If the cut isn't into the line core, you can probably repair it. If you're a fly tier, use your thread bobbin to fill the cut with fine thread. (Or borrow one from a fly tying buddy.) Hold the line horizontally on either side of the cut, and swing the bobbin like a yo-yo in rotations around the line cut. Use a pull loop to bury the thread end, like adding a new guide to a rod blank. Cover the thread with thin glue or cement. If you can't save the line's tip, keep the line and splice in a section of sinking line to make it a useable sink-tip.