Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Hellmann et al., Nat. Commun. 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture, such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighboring grid elements followed by the cascading splitting of the others, distant elements, and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.