Cosmic ray (CR) interactions can be a challenging source of background for neutrino oscillation and cross-section measurements in surface detectors. We present methods for CR rejection in measurements of charged-current quasielastic-like (CCQE-like) neutrino interactions, with a muon and a proton in the final state, measured using liquid argon time projection chambers (LArTPCs). Using a sample of cosmic data collected with the MicroBooNE detector, mixed with simulated neutrino scattering events, a set of event selection criteria is developed that produces an event sample with minimal contribution from CR background. Depending on the selection criteria used a purity between 50 and 80% can be achieved with a signal selection efficiency between 50 and 25%, with higher purity coming at the expense of lower efficiency. While using a specific dataset and selection criteria values optimized for the MicroBooNE detector, the concepts presented here are generic and can be adapted for various studies of exclusive nu mu CCQE interactions in LArTPCs.