The free surface is shown to be one of the key factors that may promote supershear rupture propagation on strike‐slip faults even if its initial shear stress is not larger enough as predicted by the Burridge‐Andrews mechanism. However, previous study has shown the free surface‐induced supershear rupture may be unsustained, which turns to sub‐Rayleigh rupture itself as the rupture propagates. We study the near‐field ground motion of sustained and unsustained supershear ruptures using the finite difference method based on the dynamic rupture processes of three vertical strike‐slip faults with the same initial stresses and different hypocenter depths. Both the unsustained supershear ruptures with shallower hypocenter depths show the sub‐Rayleigh characteristics in the peak ground velocity distribution, that is, strong amplitude is noticed beyond the end of the fault without any observed Mach cone. We observe that the arrival time differences between the maximum fault‐perpendicular and fault‐parallel velocity reveal the Mach cone clearly for the sustained supershear rupture. A distinct supershear phase in the high‐frequency seismograms is observed. We also compare the 70° dip strike‐slip case in which unsustained supershear rupture may still present sub‐Rayleigh characteristics in the near‐field ground motion, and the break of symmetry perturbs the normal stress as rupture propagates, which has a key influence in the rupture propagation and ground motion. Our work provides a new insight to understand the supershear rupture in nature earthquakes and the relationship between the ground motion and the rupture process on the fault.