Hi; by 'neck adjustment nut' I'm guessing you mean the truss rod adjustment that you find on guitars. Because of the short neck, many mandolins don't have a truss rod, and in any case, it shouldn't really be the first port of call when looking to lower the action. The truss rod alters 'neck relief', rather than just the action.
On resonator mandolins there is usually either a single screw or a pair of screws close to, or on the bridge, and this can be used to lower the bridge height. Lower it until it buzzes, then raise it a bit. If the action is still too high, especially on the lower frets, then the nut needs some attention. I would take the instrument to a decent luthier for a setup at this stage, as cutting and adjusting a nut is tricky and really needs the proper tools to get decent results. Hope this helps.
Tim