The exposed strands are from the compressionless housing, not the cable itself, but are nonetheless essential for reliable indexed shifting. The ferrule may be intact (hard to tell from the picture), and you may simply need to fix the housing. Unclamp the cable from the derailleur and slide the housing off the cable. Use a good cable cutter to trim the damaged end of the housing, file or grind the end of the housing so its evenly perpendicular to the axis of the housing, fit a new end cap, insert the cable and slide the housing back on until it seats in the ferrule. Re-connect the cable to the derailleur and adjust cable tension to achieve proper shifting.