Context. Rayleigh scattering in a hydrogen-dominated exoplanet atmosphere can be detected using ground- or space-based telescopes. However, stellar activity in the form of spots can mimic Rayleigh scattering in the observed transmission spectrum. Quantifying this phenomena is key to our correct interpretation of exoplanet atmospheric properties. Aims: We use the ten-meter Gran Telescopio Canarias (GTC) telescope to carry out a ground-based transmission spectra survey of extrasolar planets to characterize their atmospheres. In this paper we investigate the exoplanet HAT-P-11b, a Neptune-sized planet orbiting an active K-type star. Methods: We obtained long-slit optical spectroscopy of two transits of HAT-P-11b with the Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) on August 30, 2016 and September 25, 2017. We integrated the spectrum of HAT-P-11 and one reference star in several spectroscopic channels across the λ 400-785 nm region, creating numerous light curves of the transits. We fit analytic transit curves to the data taking into account the systematic effects and red noise present in the time series in an effort to measure the change of the planet-to-star radius ratio (Rp/Rs) across wavelength. Results: By fitting both transits together, we find a slope in the transmission spectrum showing an increase of the planetary radius towards blue wavelengths. Closer inspection of the transmission spectrum of the individual data sets reveals that the first transit presents this slope while the transmission spectrum of the second data set is flat. Additionally, we detect hints of Na absorption on the first night, but not on the second. We conclude that the transmission spectrum slope and Na absorption excess found in the first transit observation are caused by unocculted stellar spots. Modeling the contribution of unocculted spots to reproduce the results of the first night we find a spot filling factor of δ = 0.62-0.17+0.20 and a spot-to-photosphere temperature difference of ΔT = 429-299+184 K. Transit light curves are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/622/A172