How to fix deadbolt lever that doesn't lock or unlock the deadbolt
There's a rod (usually flat steel) that connects the throw lever to the bolt. It's probably broken. (Or maybe, less likely, the connection between the lever and the rod has stripped.)
So, yes, you can take the lock apart and see. You can probably reassemble the lock (and lock your door) without the rod while you take the part to a lock specialist.