Polar codes are a class of linear error-correction codes that have received a lot of attention due to their ability to achieve channel capacity in an arbitrary binary discrete memoryless channel (B-DMC) with low-complexity successive-cancellation (SC) decoding. However, practical implementations often require better error-correction performance than what SC decoding provides, particularly at short to moderate code lengths. Successive-cancellation flip (SCF) decoding algorithm was proposed to improve error-correction performance with an aim to detect and correct the first wrongly estimated bit in a codeword before resuming SC decoding. At each additional SC decoding trial, i.e., decoding attempt beyond the initial unsuccessful trial, one bit estimated as the least reliable is flipped. Dynamic SCF (DSCF) is a variation of SCF, where multiple bits may be flipped simultaneously per trial. Despite the improved error-correction performance compared to the SC decoder, SCF-based decoders have variable execution time, which leads to high average execution time and latency. In this work, we propose the generalized restart mechanism (GRM) that allows to skip decoding computations that are identical between the initial trial and any additional trial. Under DSCF decoding with up to 3-bit flips per decoding trial, our proposed GRM is shown to reduce the average execution time by 25% to 60% without any negative effect on error-correction performance. The proposed mechanism is adaptable to state-of-the-art latency-reduction techniques. When applied to Fast-DSCF-3 decoding, the additional reduction brought by the GRM is 15% to 22%. For the DSCF-3 decoder, the proposed mechanism requires approximately 4% additional memory.