A DNA nick, defined as a discontinuity in a double-stranded DNA molecule where the phosphodiester bond between adjacent nucleotides of one strand is absent due to enzyme action, serves as an effective mechanism to alleviate stress in supercoiled DNA. This stress release is essential for the smooth operation of transcriptional machinery. However, the underlying mechanisms and their impact on protein search dynamics, which are crucial for initiating transcription, remain unclear. Through extensive computer simulations, we unravel the molecular picture, demonstrating that intramolecular stress release due to a DNA nick is driven by a combination of writhing and twisting motions, depending on the nick's position. This stress release is quantitatively manifested as a step-like increase in the linking number. Furthermore, we elucidate that the nicked supercoiled minicircles exhibit enhanced torsional dynamics, promoting rapid conformational changes and frequent shifts in the identities of juxtaposed DNA sites on the plectoneme. The dynamics of the juxtaposition sites facilitates communication between protein and DNA, resulting in faster protein diffusion compared with native DNA with the same topology. Our findings highlight the mechanistic intricacies and underscore the importance of DNA nicks in facilitating transcription elongation by actively managing torsional stress during DNA unwinding by the RNA polymerase.