We introduce SpectraPyle, a versatile spectral stacking pipeline developed for the Euclid mission's NISP spectroscopic surveys, aimed at extracting faint emission lines and spectral features from large galaxy samples in the Wide and Deep Surveys. Designed for computational efficiency and flexible configuration, SpectraPyle supports the processing of extensive datasets critical to Euclid's non-cosmological science goals. We validated the pipeline using simulated spectra processed to match Euclid's expected final data quality. Stacking enables robust recovery of key emission lines, including Hα, Hβ, [O III], and [N II], below individual detection limits. However, the measurement of galaxy properties such as star formation rate, dust attenuation, and gas-phase metallicity are biased at stellar mass below log10(M/ M☉)̃9 due to the flux-limited nature of Euclid spectroscopic samples, where spectra below the detection threshold lack reliable redshift measurements, preventing effective stacking. The star formation rate─stellar mass relation of the parent sample is recovered reliably only in the deep survey for log10(M/ M☉)≳10, whereas the metallicity─mass relation is recovered more accurately over a wider mass range. These limitations are caused by the increased fraction of redshift measurement errors at lower masses and fluxes. We examined the impact of residual redshift contaminants that arises from mis-identified emission lines and noise spikes, on stacked spectra. Even after stringent quality selections, low-level contamination (< 6%) has minimal impact on line fluxes due to the systematically weaker emission of contaminants. A percentile-based analysis of stacked spectra provides a sensitive diagnostic for detecting contamination via coherent spurious features at characteristic wavelengths. While our simulations include most instrumental effects, real Euclid data will require a further refinement of contamination mitigation strategies.