Tidal disruptions are extremely powerful phenomena that have been designated as candidate sources of ultra-high-energy cosmic rays. The disruption of a star by a black hole can naturally provide protons and heavier nuclei, which can be injected and accelerated to ultra-high energies within a jet. Inside the jet, accelerated nuclei are likely to interact with a dense photon field, leading to a significant production of neutrinos and secondary particles. We model numerically the propagation and interactions of high-energy nuclei in jetted tidal disruption events in order to evaluate consistently their signatures in cosmic rays and neutrinos. We propose a simple model of the light curve of tidal disruption events, consisting of two stages: a high state with bright luminosity and short duration and a medium state, less bright and longer lasting. These two states have different impacts on the production of cosmic rays and neutrinos. In order to calculate the diffuse fluxes of cosmic rays and neutrinos, we model the luminosity function and redshift evolution of jetted tidal disruption events. We find that we can fit the latest ultra-high-energy cosmic-ray spectrum and composition results of the Auger experiment for a range of reasonable parameters. The diffuse neutrino flux associated with this scenario is found to be subdominant, but nearby events can be detected by IceCube or next-generation detectors such as IceCube-Gen2.