Do not use tape as a repair for a damaged appliance supply cable. Keep the disposer out of use and arrange the appropriate qualified replacement or assessment required by its manufacturer.
What the observation tells you
A split outer covering, crushed section or pulled connection may conceal damage that cannot be judged from the outside. Moving the cable until the motor works is not a safe workaround. If the area is wet, avoid handling it and isolate from a safe dry location where possible.
A useful next step
Explain how the damage occurred and whether the cable was trapped by cabinet contents. Keep access clear without disturbing the damaged connection.
Manuals and supporting guidance
Model-specific instructions take priority. These references support the practical principles discussed here; they do not diagnose your appliance.