Being a mechanical numpty, I have the following opinion:
Everything you've said seems like the clutch just isn't disengaging properly. That being said, try to adjust the cable (if you have enough left), and change the oil since the SV uses a wet clutch.
If that fails, I'd rather try a new clutch cable than a whole new clutch.
If all else fails, I'd say, yes, you need a new clutch. But then again, I'm a mechanical numpty! I'm sure those with more knowledge will be along shortly
