We perform direct numerical simulations of elastoviscoplastic (EVP) duct flows at particle volume fractions up to φ = 15 %. Unlike Newtonian suspensions, which exhibit pronounced drag increase with particle loading, EVP suspensions show only modest drag growth in dilute and semi-dilute conditions and achieve significant drag reduction relative to their Newtonian counterparts beyond a threshold φ that increases with the Bingham number. This behaviour results from two coupled mechanisms: viscoelasticity drives particles away from the walls towards the duct core, and the unyielded plug traps them with negligible slip, thereby minimising their stress contribution. As a consequence, the mean velocity profile remains largely independent of solid volume fraction, with viscous and elastic stresses nearly unchanged. In addition, we observe pronounced shear thinning in viscoelastic and EVP suspensions, in contrast to earlier predictions. These findings demonstrate that accurate drag prediction requires explicit modelling of the local solid fraction in EVP particle-laden flows.