We report the spectroscopic confirmation and fundamental properties of TOI-757 b, a mini-Neptune on a 17.5-day orbit transiting a bright star (V=9.7mag) discovered by the TESS mission. We acquired high-precision radial velocity measurements with the HARPS, ESPRESSO, and PFS spectrographs to confirm the planet detection and determine its mass. We also acquired space-borne transit photometry with the CHEOPS space telescope to place stronger constraints on the planet radius, supported with ground-based LCOGT photometry. WASP and KELT photometry were used to help constrain the stellar rotation period. We also determined the fundamental parameters of the host star. We find that TOI-757 b has a radius of R_p_=2.5+/-0.1R_{Earth} and a mass of M_p=10.5^+2.2^-2.1_M{Earth}, implying a bulk density of {rho}_p=3.6+/-0.8g/cm^3^. Our internal composition modeling was unable to constrain the composition of TOI-757 b, highlighting the importance of atmospheric observations for the system. We also find the planet to be highly eccentric with e=0.39^+0.08^-0.07, making it one of the very few highly eccentric planets among precisely characterized mini-Neptunes. Based on comparisons to other similar eccentric systems, we find a likely scenario for TOI-757 b's formation to be high eccentricity migration due to a distant outer companion. We additionally propose the possibility of a more intrinsic explanation for the high eccentricity due to star-star interactions during the earlier epoch of the Galactic disk formation, given the low metallicity and older age of TOI-757.
