At muon colliders, muon decays naturally produce intense electrons and positrons with unique features, namely high energies, high repetition rates, and small intrinsic uncertainties, that are unavailable at existing accelerator facilities. We quantitatively study the feasibility of extracting such particles in two representative future muon collider designs, IMCC and µTRISTAN. Using Monte Carlo simulations with the corresponding design parameters, we study the spatial, angular, and energy distributions of decay electrons and positrons in the curved sections of the collider ring. We find that typical deflections of 0.1–10 mrad can be achieved even for high-energy electrons carrying large energy fractions (≃ 0.6–1.0) of the muon beam energy, with the ring bending magnets (or magnets providing an equivalent field) effectively serving as a “pre-septum magnet” that partially deflects the beam before the main septum magnet, suggesting that the extraction scheme could be practically feasible. Exploiting the distinct beam properties of IMCC and µTRISTAN, we propose complementary search strategies — missing energy and momentum searches for dark matter at µTRISTAN and visible-decay searches for axion-like particles and light scalars at IMCC — which probe parameter space beyond the reach of current and other proposed experiments.