In the known topological semimetals, conventional charge carriers exist in addition to relativistic quasiparticles, and thus a disentangling of their conduction properties remains challenging. Here, we address an unsaturated extreme magnetoresistance (XMR) with a marked deviation from the semiclassical B2 behavior that is commonly credited to the presence of topologically protected electronic states. For the topologically trivial semimetal LuAs, we observe a nonsaturating XMR with a nonquadratic magnetic-field dependence gained up to nearly 60 T. Remarkably, this diamagnetic material exhibits a very large magnetostriction that provides solid evidence for a field-dependent variation of electron and hole concentrations. We show that an underlying strain-induced change in the charge-carrier densities can give rise to an unsaturated XMR even in a moderately imbalanced semimetal. Our finding is of importance as well for topological semimetals in which the number of conventional charge carriers can be continuously altered with increasing field, and hence some of their high-field properties may not necessarily reflect the presence of massless quasiparticles.