Magnetic field will produce induced current, which will produce new magnetic field. So according to the law of conservation of energy, is the energy of the original magnetic field all induced?
Your understanding is right. When energy is conserved, the energy of the primary magnetic field will decrease, or other energy (such as mechanical energy) will decrease. There may be a field source releasing energy. It may also be the magnetic field energy released by the change of the relative position of the magnet.
To sum up, the original magnetic field may not disappear.