You can change gears without the clutch, but downshifting is trickier than upshifting and starting from a stop is a whole different matter. You'd pretty much have to kill the engine at every stop and get it rolling in first gear with the starter motor.
None of this is good for any of the associated parts: shift forks, dogs, starter motor, ring gear. Once you get the bike safely home I'd leave it there until you fix the problem.
If the clutch cable is fraying at the handlebar lever, you should make sure that the round widget can rotate freely. When they don't, the clutch cable strands get fatigued, start to break, and soon after that the whole thing snaps. A replacement cable will live a short life if that problem isn't fixed.
Since your cable is as good as dead, I'd just take it off the bike and bring that to your tractor supply place.
Unfortunately, though, I'd be looking at the clutch arm on the back of the transmission since your cable isn't totally broken and the clutch isn't working.
-I'd check the lower adjustment bolt and make sure the clutch arm still has good threads for it to screw into.
-Make sure the clutch arm pivot is still mounted through the clutch arm and the two ears on the back of the transmission.
-Make sure both of those ears are still there.
-after that, start taking the throwout parts out of the back of the transmission and look for anything obviously wrong.