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We investigate the formation and evolution of misaligned accretion discs around the secondary component of a binary through mass transfer driven by Kozai-Lidov (KL) oscillations of the circumprimary disc's eccentricity and inclination. We perform smoothed particle hydrodynamics simulations to study the amount of mass transferred to the secondary star as a function of both the disc and binary parameters. For the range of parameters we explore, we find that increasing the disc aspect ratio, viscosity parameter, and initial inclination as well as decreasing the binary mass ratio leads to larger amount of mass transfer, up to a maximum of about 10 % of the initial mass of the primary disc. The circumsecondary disc forms with a high eccentricity and a high inclination and is also able to undergo KL oscillations. The circumsecondary disc oscillations have a shorter period than those in the disc around the primary. We find that some of the material that escapes the Roche lobe of the two components forms a misaligned circumbinary accretion disc. This study has implications for disc evolution in young binary star systems.